Find the HCF of 1008 and 1080 by prime factorization.

The largest possible number which divides the given numbers exactly without leaving any remainder is called the HCF (Highest Common Factor).

Answer: HCF of 1008 and 1080 by prime factorization is 72

HCF of 1008 and 1080 is the highest number that divides 1008 and 1080 exactly leaving the remainder 0.

Explanation:

We will show the prime factorization method to find the highest common factor of 1008 and 1080.

HCF of 1008 and 1080 by Prime Factorization

Let us represent 1008 and 1080 as a product of its prime factors.

Prime factorization of 1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

Prime factorization of 1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5

Observe that the common factors in the prime factorization of 1008 and 1080 are 2, 2, 2, 3, and 3.

So, HCF of 1008 and 1080 is 2 × 2 × 2 × 3 × 3 = 72

Therefore, the HCF of 1008 and 1080 is 72.