# What is the GCF of 14 and 35?

GCF (Greatest Common Factor) of two or more numbers would be the largest possible number that divides the given numbers exactly without any remainder(0 as remainder).

## Answer: GCF of 14 and 35 is 7

Two methods to find the GCF of 14 and 35 are explained below.

## Methods to find GCF of 14 and 35

- Prime factorization Method
- Long division Method

### Method1: GCF of 14 and 35 by Prime Factorization

Let us write 14 and 35 as a product of their prime factors.

Prime factorization of 14 is 2 × 7

Prime factorization of 35 is 5 × 7

Common factors = 7

GCF is the product of the factors that are common to each of the given numbers.

GCF(14,35) is 7

### Method2: GCF of 14 and 35 by Long Division

- Step 1: Divide 35 by 14 and check the remainder.
- Step 2: The remainder of the above step will now act as the divisor and the divisor of the above step as the dividend and perform the long division again.
- Step 3: Long division is performed untill a 0 is obtained as the remainder.

### Therefore, GCF of 14 and 35 is 7

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