# What is the GCF of 36 and 40?

GCF (Greatest Common Factor) of 36 and 40 is the largest possible number which divides the numbers 36 and 40 exactly leaving the remainder as 0

## Answer: GCF of 36 and 40 is 4

We can find the GCF by the following two methods.

## Explanation:

The greatest common factor of 36 and 40 is the greatest number which divides the numbers 36 and 40 exactly.

- GCF of 36 and 40 by Long Division
- GCF of 36 and 40 by Prime Factorization

### Method 1: GCF of 36 and 40 by Long Division

**Step 1:** Divide 36 by 40 and check the remainder. Here, the remainder is 4

**Step 2:** Make the remainder 4 as the divisor and the divisor 36 as the dividend and perform the long division again.

**Step 3:** Continue till you get the remainder as 0 and the last divisor of the division process will be the GCF(36, 40)

### Method 2: GCF of 36 and 40 by Prime Factorization

We will express the numbers 36 and 40 as a product of their prime factors.

Prime factorization of 36 is 2 × 2 × 3 × 3

Prime factorization of 40 is 2 × 2 × 2 × 5

The common factors in both prime factorization = 2 × 2

GCF is the product of the prime factors that are common to the prime factorization of 36 and 40

So, GCF of 36 and 40 is 4

You can find the GCF in any of the above methods but the solution will be the same.