What is the Greatest Common Factor of 13725 and 13730?

Greatest common factor (GCF) of 13725 and 13730 is 5.

GCF(13725,13730) = 5

We will now calculate the prime factors of 13725 and 13730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13725 and 13730.

How to find the GCF of 13725 and 13730?

We will first find the prime factorization of 13725 and 13730. After we will calculate the factors of 13725 and 13730 and find the biggest common factor number .

Step-1: Prime Factorization of 13725

Prime factors of 13725 are 3, 5, 61. Prime factorization of 13725 in exponential form is:

13725 = 3² × 5² × 61¹

Step-2: Prime Factorization of 13730

Prime factors of 13730 are 2, 5, 1373. Prime factorization of 13730 in exponential form is:

13730 = 2¹ × 5¹ × 1373¹

Step-3: Factors of 13725

List of positive integer factors of 13725 that divides 13725 without a remainder.

1, 3, 5, 9, 15, 25, 45, 61, 75, 183, 225, 305, 549, 915, 1525, 2745, 4575

Step-4: Factors of 13730

List of positive integer factors of 13730 that divides 13725 without a remainder.

1, 2, 5, 10, 1373, 2746, 6865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13725 and 13730. The biggest common factor number is the GCF number.
So the greatest common factor 13725 and 13730 is 5.

Also check out the Least Common Multiple of 13725 and 13730