IGCSE Maths 0580 Types of Number Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Number · 1.1

Every types of number question from 24 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 1.1. 41 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Number past paper questions.

0580 Types of Number past paper questions: Core (Papers 1 and 3)

15 marksCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q1

From this list of numbers: 1.694, √18, 6, 6.666, 7, √225, 25, 27, 39, 56, 1000

write down (a) an even number (b) a factor of 28 (c) a square number (d) a prime number (e) an irrational number.

Show solution
Part (a)
  1. An even number divides exactly by 2 (it ends in 0, 2, 4, 6 or 8).
  2. Even number: 6 (56 or 1000 are also correct)
Answer 6
Part (b)
  1. A factor of 28 divides into 28 with no remainder. 28 ÷ 7 = 4.
  2. Factor of 28: 7
Answer 7
Part (c)
  1. A square number is a whole number multiplied by itself. 25 = 5 × 5.
  2. Square number: 25
  3. Tip: √225 = 15, and 15 is not a square number.
Answer 25
Part (d)
  1. A prime number has exactly two factors: 1 and itself. 7 has only the factors 1 and 7.
  2. Prime number: 7
Answer 7
Part (e)
  1. An irrational number cannot be written as a fraction. The square root of a number that is not a perfect square is irrational.
  2. 18 is not a perfect square, so the irrational number is √18
Answer √18
23 marksCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q16

Buses leave every 16 minutes for Alve and every 28 minutes for Riba. At 08 25 a bus for Alve and a bus for Riba leave the station together. Find the next time a bus for Alve and a bus for Riba leave the station together.

Show solution
  1. The buses leave together again after a time that is a multiple of both 16 and 28, so find the LCM.
  2. Prime factors: 16 = 2⁴ and 28 = 2² × 7.
  3. LCM = 2⁴ × 7 = 16 × 7 = 112 minutes.
  4. 112 minutes = 60 + 52 = 1 hour 52 minutes.
  5. 08 25 + 1 h 52 min = 09 25 + 52 min = 10 17
Answer 10 17
32 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q16

Find the value of the reciprocal of 0.8.

Show solution
  1. The reciprocal of a number is 1 divided by that number.
  2. 1 ÷ 0.8 = 1⁄0.8 = 10⁄8 (multiply top and bottom by 10).
  3. 10⁄8 = 1.25, so the reciprocal is 1.25
Answer 1.25
41 markCore

May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q1

Write down the number that is 1 more than 4 999 499.

Show solution
  1. Add 1 to the units digit: 9 + 1 = 10, so the units become 0 and 1 is carried to the tens.
  2. The tens digit is 9, so 9 + 1 = 10: the tens become 0 and 1 is carried to the hundreds.
  3. The hundreds digit is 4, so 4 + 1 = 5.
  4. 4 999 499 + 1 = 4 999 500
Answer 4 999 500
51 markCore

May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q2

Write the number 707 700 in words.

Show solution
  1. Split the number at the thousands: 707 700 = 707 thousand + 700.
  2. 707 = seven hundred and seven, and 700 = seven hundred.
  3. In words: seven hundred and seven thousand, seven hundred
Answer seven hundred and seven thousand, seven hundred
64 marksCore

May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q19

(a) Write 84 as a product of its prime factors.

(b) 96 can be written as 2ᴾ × 3. Find the value of P.

(c) Use your answers to (a) and (b) to find the lowest common multiple (LCM) of 84 and 96. Leave your answer as a product of prime numbers.

Show solution
Part (a)
  1. Divide by primes until you reach 1: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7, 7 ÷ 7 = 1.
  2. 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Answer 2² × 3 × 7
Part (b)
  1. 96 = 2ᴾ × 3, so 2ᴾ = 96 ÷ 3 = 32.
  2. 32 = 2 × 2 × 2 × 2 × 2 = 2⁵, so P = 5
Answer P = 5
Part (c)
  1. For the LCM take the highest power of each prime from either number.
  2. 2: highest is 2⁵ (from 96). 3: 3¹ in both. 7: 7¹ (from 84).
  3. LCM = 2⁵ × 3 × 7
Answer 2⁵ × 3 × 7
71 markCore

May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q14

Write down the reciprocal of 5⁄7.

Show solution
  1. The reciprocal of a fraction is the fraction turned upside down.
  2. Reciprocal of 5⁄7 = 7⁄5 (= 1.4)
Answer 7⁄5
81 markCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q1

Write the number four hundred thousand and fifty-three in figures.

Show solution
  1. Split the number into parts: four hundred thousand = 400 000 and fifty-three = 53.
  2. Add them: 400 000 + 53 = 400 053
  3. Tip: There are no thousands apart from the 400, so the thousands columns hold zeros.
Answer 400 053
93 marksCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q2

(a) Write down the multiple of 9 between 50 and 60. (b) Write down all the common factors of 20 and 30.

Show solution
Part (a)
  1. List the multiples of 9: 9, 18, 27, 36, 45, 54, 63, …
  2. The only one between 50 and 60 is 54
Answer 54
Part (b)
  1. List the factors of 20 in pairs: 1 × 20, 2 × 10, 4 × 5. So the factors are 1, 2, 4, 5, 10, 20.
  2. List the factors of 30 in pairs: 1 × 30, 2 × 15, 3 × 10, 5 × 6. So the factors are 1, 2, 3, 5, 6, 10, 15, 30.
  3. Pick out the numbers that are in both lists: 1, 2, 5, 10
Answer 1, 2, 5, 10
101 markCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q6

Explain why 39 is not a prime number.

Show solution
  1. A prime number has exactly two factors: 1 and itself.
  2. Test small numbers: 39 ÷ 3 = 13.
  3. So 39 = 3 × 13, which means 39 also has factors 3 and 13, so it is not prime.
Answer 39 = 3 × 13
112 marksCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q22

Find the lowest common multiple (LCM) of 54 and 90.

Show solution
  1. Write each number as a product of primes: 54 = 2 × 3³ and 90 = 2 × 3² × 5.
  2. For the LCM, take the highest power of every prime that appears: 2, 3³ and 5.
  3. LCM = 2 × 27 × 5 = 270
  4. Check: 270 ÷ 54 = 5 and 270 ÷ 90 = 3 ✓
Answer 270
121 markCore

May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q25

Draw a ring around any irrational numbers that are in the list: 3317760.25, √0.4, 7⁄13, 6432.89¹⁷

Show solution
  1. A rational number can be written as a fraction. Check each one.
  2. 3317760.25 is the fourth root of 331776. The calculator gives 24, so it is rational.
  3. 7⁄13 is already a fraction, so it is rational.
  4. 6432.89¹⁷ is a terminating decimal raised to a whole-number power, so it is rational.
  5. √0.4 = √2⁄5. 0.4 is not a square of any fraction, so the decimal never ends or repeats.
  6. Ring √0.4
Answer √0.4
132 marksCore

May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q2

Write down all the factors of 26.

Show solution
  1. Find the factors in pairs that multiply to 26.
  2. 1 × 26 and 2 × 13. (No other whole numbers divide 26.)
  3. Write them in order: 1, 2, 13, 26
Answer 1, 2, 13, 26
142 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q8

Write down the two prime numbers that are greater than 20 but less than 30.

Show solution
  1. Check each number from 21 to 29.
  2. 21 = 3 × 7, 22, 24, 26 and 28 are even, 25 = 5 × 5, 27 = 3 × 9.
  3. 23 and 29 have only the factors 1 and themselves, so they are prime.
  4. 23 and 29
Answer 23 and 29
151 markCore

Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q1

Write the number 8017 in words.

Show solution
  1. Split the number: 8017 = 8 thousand + 17.
  2. In words: eight thousand and seventeen
Answer eight thousand and seventeen
163 marksCore

Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q23

Two buses leave the bus station at 08 00. One returns to the station every 34 minutes. The other returns to the station every 30 minutes. Work out the time they will first return to the station together.

Show solution
  1. The buses are both back at the station after a time that is a multiple of 34 and of 30, so find the LCM.
  2. 34 = 2 × 17 and 30 = 2 × 3 × 5.
  3. LCM = 2 × 3 × 5 × 17 = 510 minutes.
  4. 510 minutes = 8 × 60 + 30 = 8 hours 30 minutes.
  5. 08 00 + 8 h 30 min = 16 30
Answer 16 30
173 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q4

(a) Write down all the factors of 24. (b) Write down the reciprocal of 3⁄7.

Show solution
Part (a)
  1. Find factor pairs that multiply to 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6.
  2. 5 does not divide into 24, and the next number, 6, is already in the list, so stop.
  3. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Answer 1, 2, 3, 4, 6, 8, 12, 24
Part (b)
  1. The reciprocal of a fraction is the fraction turned upside down.
  2. Reciprocal of 3⁄7 = 7⁄3
Answer 7⁄3
181 markCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q1

Write down the value of the 3 in the number 23 679.

Show solution
  1. Write the place-value columns: 23 679 = 2 ten-thousands, 3 thousands, 6 hundreds, 7 tens, 9 units.
  2. The 3 is in the thousands column, so its value is 3000
Answer 3000
193 marksCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q8

A number, n, is a factor of 144 and a multiple of 9. Find all the values for n.

Show solution
  1. n must divide 144 exactly and also be in the 9 times table.
  2. 144 = 9 × 16, so n is 9 multiplied by a factor of 16.
  3. The factors of 16 are 1, 2, 4, 8 and 16.
  4. 9 × 1 = 9, 9 × 2 = 18, 9 × 4 = 36, 9 × 8 = 72, 9 × 16 = 144.
  5. 9, 18, 36, 72, 144
Answer 9, 18, 36, 72, 144
205 marksCore

Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q22

(a) A train to town P leaves a station every 20 minutes. A train to town Q leaves every 35 minutes. Both trains leave at 09 30. Find the next time both trains leave together.

(b) The distance, d km, between town P and town Q is 97 km, correct to the nearest kilometre. Complete the statement … ≤ d < …

Show solution
Part (a)
  1. The trains leave together again after a time that is a multiple of both 20 and 35, so find the LCM.
  2. 20 = 2² × 5 and 35 = 5 × 7, so LCM = 2² × 5 × 7 = 140 minutes.
  3. 140 minutes = 2 hours 20 minutes.
  4. 09 30 + 2 h 20 min = 11 50
Answer 11 50
Part (b)
  1. Correct to the nearest kilometre means the true value is within 0.5 km of 97.
  2. Lower bound = 97 − 0.5 = 96.5. Upper bound = 97 + 0.5 = 97.5.
  3. 96.5 ≤ d < 97.5
Answer 96.5 ≤ d < 97.5
212 marksCore

Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q2

Write down all the factors of 32.

Show solution
  1. Find the factors in pairs that multiply to 32.
  2. 1 × 32, 2 × 16, 4 × 8. (3, 5, 6 and 7 do not divide 32.)
  3. Write them in order: 1, 2, 4, 8, 16, 32
Answer 1, 2, 4, 8, 16, 32
223 marksCore

Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q6

From the list 0, 1, 8, 27, 39, 51, 59, 81, write down (a) a square number (b) the value of 39⁰ (c) a prime number.

Show solution
Part (a)
  1. A square number is a whole number times itself. 81 = 9 × 9.
  2. 81 (0 = 0² and 1 = 1² are also correct)
Answer 81
Part (b)
  1. Any non-zero number to the power 0 is 1.
  2. 39⁰ = 1
Answer 1
Part (c)
  1. Check each number for factors other than 1 and itself.
  2. 27 = 3 × 9, 39 = 3 × 13, 51 = 3 × 17 and 81 = 9 × 9 are not prime. 59 has no other factors.
  3. 59
Answer 59
232 marksCore

Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q1

Write down all the factors of 26.

Show solution
  1. Find the factors in pairs that multiply to 26.
  2. 1 × 26 and 2 × 13. (No other whole numbers divide 26.)
  3. Write them in order: 1, 2, 13, 26
Answer 1, 2, 13, 26
242 marksCore

Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q25

Find the lowest common multiple (LCM) of 20 and 36.

Show solution
  1. Write each number as a product of primes: 20 = 2² × 5 and 36 = 2² × 3².
  2. For the LCM, take the highest power of every prime that appears: 2², 3² and 5.
  3. LCM = 4 × 9 × 5 = 180
  4. Check: 180 ÷ 20 = 9 and 180 ÷ 36 = 5 ✓
Answer 180
254 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q4

7, 27, 39, 49, 99, 112

From the list of numbers, write down (a) an even number (b) a square number (c) a factor of 56 (d) a prime number.

Show solution
Part (a)
  1. An even number ends in 0, 2, 4, 6 or 8. Only 112 does.
  2. Even number: 112
Answer 112
Part (b)
  1. A square number is a whole number times itself. 7 × 7 = 49.
  2. Square number: 49
Answer 49
Part (c)
  1. A factor of 56 divides into 56 exactly. 56 ÷ 7 = 8.
  2. Factor of 56: 7
Answer 7
Part (d)
  1. A prime number has exactly two factors, 1 and itself.
  2. 27 = 3 × 9, 39 = 3 × 13, 49 = 7 × 7, 99 = 9 × 11 and 112 is even, so none of these are prime.
  3. 7 has only the factors 1 and 7, so the prime number is 7
Answer 7
261 markCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q5

Write down the reciprocal of 5.

Show solution
  1. The reciprocal of a number is 1 divided by that number.
  2. Reciprocal of 5 = 1 ÷ 5 = 1⁄5 (or 0.2)
Answer 1⁄5
273 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q22

A = 2³ × 3, B = 3² × 5

(a) Find the highest common factor (HCF) of A and B.

(b) Find the lowest common multiple (LCM) of A and B.

Show solution
Part (a)
  1. A = 2 × 2 × 2 × 3 and B = 3 × 3 × 5.
  2. The only prime factor in both lists is one 3.
  3. HCF = 3
Answer 3
Part (b)
  1. For the LCM take the highest power of each prime that appears in either number: 2³, 3² and 5.
  2. LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360
Answer 360
281 markCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q1

Write the number sixteen thousand and sixty-two in figures.

Show solution
  1. Sixteen thousand = 16 000.
  2. Add sixty-two: 16 000 + 62 = 16 062
Answer 16 062
292 marksCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q18

Find the highest common factor (HCF) of 66 and 110.

Show solution
  1. Write each number as a product of primes: 66 = 2 × 3 × 11 and 110 = 2 × 5 × 11.
  2. The primes in both lists are 2 and 11.
  3. HCF = 2 × 11 = 22
Answer 22
302 marksCore

May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q20

Find the highest common factor (HCF) of 36 and 54.

Show solution
  1. Write each number as a product of primes: 36 = 2 × 2 × 3 × 3 and 54 = 2 × 3 × 3 × 3.
  2. Find the primes they share: one 2 and two 3s.
  3. HCF = 2 × 3 × 3 = 18
Answer 18

0580 Types of Number past paper questions: Extended (Papers 2 and 4)

313 marksExtended

May/June 2026 · Paper 2 · 0580/21/M/J/26 · Q10

(a) 24 192 = 2⁷ × 3³ × 7 and 245 000 = 2³ × 5⁴ × 7². Find the highest common factor (HCF) of 24 192 and 245 000.

(b) A number, k, is written as k = 2³ × 3⁴ × 5 × c², where c is a prime number greater than 5. Write the number 20k² as a product of its prime factors, in terms of c in its simplest form.

Show solution
Part (a)
  1. The HCF uses only the primes in both numbers, each with its lowest power.
  2. 2 appears as 2⁷ and 2³: use 2³. 7 appears as 7 and 7²: use 7. 3 and 5 are not in both.
  3. HCF = 2³ × 7 = 8 × 7 = 56
Answer 56
Part (b)
  1. Square k by doubling every power: k² = 2⁶ × 3⁸ × 5² × c⁴.
  2. Write 20 as primes: 20 = 2² × 5.
  3. Multiply by adding the powers of matching primes: 2⁶ × 2² = 2⁸ and 5² × 5 = 5³.
  4. 20k² = 2⁸ × 3⁸ × 5³ × c⁴
Answer 2⁸ × 3⁸ × 5³ × c⁴
322 marksExtended

May/June 2026 · Paper 2 · 0580/22/M/J/26 · Q3

Find the reciprocal of 31⁄3. Give your answer as a fraction in its simplest form.

Show solution
  1. Change the mixed number to an improper fraction: 31⁄3 = 3 × 3 + 1⁄3 = 10⁄3.
  2. The reciprocal is the fraction turned upside down.
  3. Reciprocal = 3⁄10
Answer 3⁄10
336 marksExtended

May/June 2026 · Paper 2 · 0580/22/M/J/26 · Q9

(a) Write 63 as a product of its prime factors.

(b) Find the lowest common multiple (LCM) of 63 and 42.

(c) Find the highest common factor (HCF) of 63a⁵c² and 42a²c⁵.

Show solution
Part (a)
  1. Divide by primes: 63 ÷ 3 = 21, 21 ÷ 3 = 7, 7 ÷ 7 = 1.
  2. 63 = 3 × 3 × 7 = 3² × 7
Answer 3² × 7
Part (b)
  1. Write 42 as primes: 42 = 2 × 3 × 7.
  2. For the LCM, take the highest power of each prime from either number: 2, 3² and 7.
  3. LCM = 2 × 9 × 7 = 126
Answer 126
Part (c)
  1. HCF of the numbers: 63 = 3² × 7 and 42 = 2 × 3 × 7 share 3 × 7 = 21.
  2. For each letter, take the lower power: a⁵ and a² give a²; c² and c⁵ give c².
  3. HCF = 21a²c²
Answer 21a²c²
343 marksExtended

May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q6

A red light flashes every 20 minutes. A blue light flashes every 35 minutes. The two lights flash together at 10 00. Find the next time that the two lights flash together.

Show solution
  1. The lights flash together again after a time that is a multiple of both 20 and 35, so find the LCM.
  2. Prime factors: 20 = 2² × 5 and 35 = 5 × 7.
  3. LCM = 2² × 5 × 7 = 4 × 5 × 7 = 140 minutes.
  4. 140 minutes = 120 + 20 = 2 hours 20 minutes.
  5. 10 00 + 2 h 20 min = 12 20
Answer 12 20
353 marksExtended

Feb/Mar 2026 · Paper 2 · 0580/22/F/M/26 · Q3(a)

From this list of numbers: −50, −11, 9, 15, 27, 50, 83, write down (i) a prime number (ii) a cube number (iii) two numbers with a product of 550.

Show solution
Part (i)
  1. A prime number has exactly two factors: 1 and itself. 83 is not divisible by 2, 3, 5 or 7.
  2. Prime number: 83
Answer 83
Part (ii)
  1. A cube number is a whole number multiplied by itself three times. 3 × 3 × 3 = 27.
  2. Cube number: 27
Answer 27
Part (iii)
  1. 550 = 50 × 11. The list has 50 and −50, 11 only as −11.
  2. Negative × negative = positive, so (−50) × (−11) = 550.
  3. −50 and −11
Answer −50 and −11
361 markExtended

Feb/Mar 2026 · Paper 4 · 0580/42/F/M/26 · Q1

Write the number seven point two five million in figures.

Show solution
  1. One million is 1 000 000.
  2. 7.25 million = 7.25 × 1 000 000 = 7 250 000
Answer 7 250 000
371 markExtended

Oct/Nov 2025 · Paper 2 · 0580/22/O/N/25 · Q2

Find all the common factors of 8 and 12.

Show solution
  1. List the factors of each number.
  2. Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12.
  3. The factors in both lists are 1, 2, 4
Answer 1, 2, 4
384 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/22/O/N/25 · Q13

M = 2⁷ × 3³ × 5². (a) Write 14M as a product of its prime factors. Give your answer in index form.

(b) R is an integer and M⁄R is a cube number. Find the smallest possible value of R.

Show solution
Part (a)
  1. Write 14 as primes: 14 = 2 × 7.
  2. Multiply: add the powers of 2 (2⁷ × 2 = 2⁸) and include the new prime 7.
  3. 14M = 2⁸ × 3³ × 5² × 7
Answer 2⁸ × 3³ × 5² × 7
Part (b)
  1. A cube number has every prime power a multiple of 3.
  2. 2⁷: the largest multiple of 3 below 7 is 6, so divide by 2¹. 3³ is already fine. 5²: divide by 5² to leave 5⁰.
  3. R = 2 × 5² = 2 × 25 = 50
  4. Check: M ÷ 50 = 2⁶ × 3³ = (2² × 3)³ = 12³ ✓
Answer 50
391 markExtended

Oct/Nov 2025 · Paper 2 · 0580/23/O/N/25 · Q2

Find the largest odd number that is a common factor of 90 and 120.

Show solution
  1. Find the highest common factor of 90 and 120: 90 = 2 × 3² × 5 and 120 = 2³ × 3 × 5, so HCF = 2 × 3 × 5 = 30.
  2. Every common factor of 90 and 120 is a factor of 30: 1, 2, 3, 5, 6, 10, 15, 30.
  3. The largest odd one is 15
Answer 15
403 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/23/O/N/25 · Q7

(a) The sum of all the prime numbers less than 10 is equal to 17. Find the sum of all the prime numbers less than 16.

(b) x is an integer. The sum of the prime numbers greater than 6 and less than x is equal to 18. Find a possible value for x.

Show solution
Part (a)
  1. The primes less than 10 are 2, 3, 5, 7 (sum 17). The primes from 10 to 16 are 11 and 13.
  2. Sum = 17 + 11 + 13 = 41
Answer 41
Part (b)
  1. The primes greater than 6 are 7, 11, 13, … Add them in order: 7 + 11 = 18.
  2. So the primes must stop at 11, which means 13 must not be included: x is more than 11 but at most 13.
  3. x = 12 (13 is also correct)
Answer x = 12
412 marksExtended

May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q8

Find the highest common factor (HCF) of 36 and 54.

Show solution
  1. Write each number as a product of primes: 36 = 2 × 2 × 3 × 3 and 54 = 2 × 3 × 3 × 3.
  2. Pick out the primes they share: one 2 and two 3s.
  3. HCF = 2 × 3 × 3 = 18
Answer 18

Question papers used on this page

All types of number questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/11/M/J/260580_s26_qp_11May/June 2026 · Paper 1 (Core)Q1, Q16
0580/12/M/J/260580_s26_qp_12May/June 2026 · Paper 1 (Core)Q16
0580/13/M/J/260580_s26_qp_13May/June 2026 · Paper 1 (Core)Q1, Q2, Q19
0580/21/M/J/260580_s26_qp_21May/June 2026 · Paper 2 (Extended)Q10
0580/22/M/J/260580_s26_qp_22May/June 2026 · Paper 2 (Extended)Q3, Q9
0580/23/M/J/260580_s26_qp_23May/June 2026 · Paper 2 (Extended)Q6
0580/31/M/J/260580_s26_qp_31May/June 2026 · Paper 3 (Core)Q14
0580/32/M/J/260580_s26_qp_32May/June 2026 · Paper 3 (Core)Q1, Q2, Q6, Q22, Q25
0580/33/M/J/260580_s26_qp_33May/June 2026 · Paper 3 (Core)Q2
0580/12/F/M/260580_m26_qp_12Feb/Mar 2026 · Paper 1 (Core)Q8
0580/22/F/M/260580_m26_qp_22Feb/Mar 2026 · Paper 2 (Extended)Q3(a)
0580/32/F/M/260580_m26_qp_32Feb/Mar 2026 · Paper 3 (Core)Q1, Q23
0580/42/F/M/260580_m26_qp_42Feb/Mar 2026 · Paper 4 (Extended)Q1
0580/11/O/N/250580_w25_qp_11Oct/Nov 2025 · Paper 1 (Core)Q4
0580/12/O/N/250580_w25_qp_12Oct/Nov 2025 · Paper 1 (Core)Q1, Q8
0580/22/O/N/250580_w25_qp_22Oct/Nov 2025 · Paper 2 (Extended)Q2, Q13
0580/23/O/N/250580_w25_qp_23Oct/Nov 2025 · Paper 2 (Extended)Q2, Q7
0580/31/O/N/250580_w25_qp_31Oct/Nov 2025 · Paper 3 (Core)Q22
0580/32/O/N/250580_w25_qp_32Oct/Nov 2025 · Paper 3 (Core)Q2, Q6
0580/33/O/N/250580_w25_qp_33Oct/Nov 2025 · Paper 3 (Core)Q1, Q25
0580/11/M/J/250580_s25_qp_11May/June 2025 · Paper 1 (Core)Q4, Q5, Q22
0580/12/M/J/250580_s25_qp_12May/June 2025 · Paper 1 (Core)Q1, Q18
0580/13/M/J/250580_s25_qp_13May/June 2025 · Paper 1 (Core)Q20
0580/22/M/J/250580_s25_qp_22May/June 2025 · Paper 2 (Extended)Q8

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