What is the Greatest Common Factor of 13575 and 13580?

Greatest common factor (GCF) of 13575 and 13580 is 5.

GCF(13575,13580) = 5

We will now calculate the prime factors of 13575 and 13580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13575 and 13580.

How to find the GCF of 13575 and 13580?

We will first find the prime factorization of 13575 and 13580. After we will calculate the factors of 13575 and 13580 and find the biggest common factor number .

Step-1: Prime Factorization of 13575

Prime factors of 13575 are 3, 5, 181. Prime factorization of 13575 in exponential form is:

13575 = 3¹ × 5² × 181¹

Step-2: Prime Factorization of 13580

Prime factors of 13580 are 2, 5, 7, 97. Prime factorization of 13580 in exponential form is:

13580 = 2² × 5¹ × 7¹ × 97¹

Step-3: Factors of 13575

List of positive integer factors of 13575 that divides 13575 without a remainder.

1, 3, 5, 15, 25, 75, 181, 543, 905, 2715, 4525

Step-4: Factors of 13580

List of positive integer factors of 13580 that divides 13575 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 97, 140, 194, 388, 485, 679, 970, 1358, 1940, 2716, 3395, 6790

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13575 and 13580. The biggest common factor number is the GCF number.
So the greatest common factor 13575 and 13580 is 5.

Also check out the Least Common Multiple of 13575 and 13580