Factoring and Multiples

# What is the greatest common factor of 25 and 36?

###### May 13, 2016 9:44AM

The GCF of 25 and 36 is 1 (one). One way to determine the

greatest common factor is to find all the factors of the numbers

and compare them.

The factors of 25 are 1, 5, and 25.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The only common factor is 1. Therefore, the greatest common

factor is 1, which means the 25 and 36 are relatively prime.

The greatest common factor can also be calculated by identifying

the common prime factors and multiplying them together.

The prime factors of 25 are 5 and 5.

The prime factors of 36 are 2, 2, 3, and 3.

There are no prime factors in common, so the numbers are

relatively prime, which means their greatest common factor is

1.

Another method is the Euclidean algorithm. 36 / 25 = 1,

remainder 11. Forget the quotient, and the divisor becomes the new

dividend, and the remainder becomes the new divisor: 25 / 11 = 2,

remainder 3. Repeat: 11 / 3 = 3rem2. 3 / 2 = 1 R 1. 2 / 1 = 2 R 0.

With no remainder, we check the last divisor: 1.

###### December 10, 2010 12:25PM

GCF of 25 and 36 is 1.

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