Number Basics (Solutions)

Number Basics — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)List factors of each, or use repeated division: 36=2²×3², 48=2⁴×3. HCF takes the lowest power of each common factor.

HCF = 2² × 3 = 12
(b)LCM takes the highest power of every prime factor present in either number.

LCM = 2⁴ × 3² = 144
Question 2

(a)Divide repeatedly by the smallest prime that fits: 72÷2=36, 36÷2=18, 18÷2=9, 9÷3=3, 3÷3=1.

72 = 2³ × 3²
Question 3

(a)List every number that divides exactly into 24.

1, 2, 3, 4, 6, 8, 12, 24
(b)A prime number has exactly two factors: 1 and itself.

2 and 3 are prime
Question 4

(a)HCF: 60=2²×3×5, 84=2²×3×7, common factors 2²×3=12. LCM = (60×84)/HCF.

HCF = 12, LCM = 5040 ÷ 12 = 420
Question 5

(a)Divide repeatedly by the smallest prime that fits.

108 = 2² × 3³
Question 6

(a)Test division by small primes: 91 ÷ 7 = 13 exactly.

91 = 7 × 13, so it is NOT prime
Question 7

(a)Take the highest power of each prime present: 8=2³, 12=2²×3, 20=2²×5.

LCM = 2³ × 3 × 5 = 120
Question 8

(a)Multiply 7 by 1, 2, 3, 4, 5.

7, 14, 21, 28, 35
Question 9

(a)An even number is exactly divisible by 2. 0 ÷ 2 = 0 exactly.

0 is even, since it divides exactly by 2
Question 10

(a)Order from smallest (most negative) to largest.

−8, −5, 0, 2, 3

Book a free trial class

Tell us a little about your requirement.