What is the HCF of 24, 12, 36 and 60?

Concept: The Highest Common Factor (HCF) of a set of numbers is the largest positive integer that divides every number in the set exactly. It is obtained via prime factorisation by multiplying, for each prime, its lowest power occurring across all the numbers.

Application: Prime factorise each given number.

1. 24 = 23 × 3

2. 12 = 22 × 3

3. 36 = 22 × 32

4. 60 = 22 × 3 × 5

5. The prime 2 appears with powers 3, 2, 2, and 2 across the four factorisations — its lowest common power is 22. The prime 3 appears with powers 1, 1, 2, and 1 — its lowest common power is 31. The prime 5 appears only in one of the four numbers, so it is not common to all of them.

So, HCF = 22 × 3 = 4 × 3 = 12.

Cross-check: Dividing each given number by 12 gives quotients 2, 1, 3, and 5 — all whole numbers, confirming 12 is a common factor of all four numbers. Also, 24 (the largest option) does not divide 12 exactly, confirming that no larger common factor exists among the given numbers.