What is the Greatest Common Factor of 13625 and 13635?

Greatest common factor (GCF) of 13625 and 13635 is 5.

GCF(13625,13635) = 5

We will now calculate the prime factors of 13625 and 13635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13625 and 13635.

How to find the GCF of 13625 and 13635?

We will first find the prime factorization of 13625 and 13635. After we will calculate the factors of 13625 and 13635 and find the biggest common factor number .

Step-1: Prime Factorization of 13625

Prime factors of 13625 are 5, 109. Prime factorization of 13625 in exponential form is:

13625 = 5³ × 109¹

Step-2: Prime Factorization of 13635

Prime factors of 13635 are 3, 5, 101. Prime factorization of 13635 in exponential form is:

13635 = 3³ × 5¹ × 101¹

Step-3: Factors of 13625

List of positive integer factors of 13625 that divides 13625 without a remainder.

1, 5, 25, 109, 125, 545, 2725

Step-4: Factors of 13635

List of positive integer factors of 13635 that divides 13625 without a remainder.

1, 3, 5, 9, 15, 27, 45, 101, 135, 303, 505, 909, 1515, 2727, 4545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13625 and 13635. The biggest common factor number is the GCF number.
So the greatest common factor 13625 and 13635 is 5.

Also check out the Least Common Multiple of 13625 and 13635