Question

PRACTICE

(c) Given (k − 2) is the highest common factor
(HCF) of 18, 36 and 54. Find the value of k.
[3 marks]​

Answer 1

k = 20

Explanation:

Expressing 18, 36 and 54 as a product of their prime factors

18 = 2 × 3 × 3 = 2 × 3²

36 = 2 × 2 × 3 × 3 = 2² × 3²

54 = 2 × 3 × 3 × 3 = 2 × 3³

The common prime factors are 2 and 3²

HCF = 2 × 3² = 2 × 9 = 18

Thus

k - 2 = 18 ( add 2 to both sides )

k = 20