# What is the gcf of 26 and 65?

GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set.

## Answer: The GCF of 26 and 65 is 13

Let us see how to find the GCF of 26 and 65

## Explanation:

Let us find the GCF using 2 methods

- Long division
- Prime factorization

### Method 1 : GCF (26,63) by Prime factorization

To calculate the GCF of 26 and 65 lets's decompose them into their respective prime factors as shown below

we see that the common factors of 26 and 65 is 13

Hence, GCF of 26 and 65 = 13

Method 2: GCF(26,65) by Long Division

We will now be looking into another method to calculate the GCF using long division method.

- Divide the largest number by the smallest number. i.e, 65 divided by 26
- Take divisor as new dividend and remainder as the new divisor, i.e. divide the first divisor by the first remainder.
- Proceed till the remainder is zero and the last divisor will be the
**GCF**of the given numbers.