What is the Greatest Common Factor of 13725 and 13734?

Greatest common factor (GCF) of 13725 and 13734 is 9.

GCF(13725,13734) = 9

We will now calculate the prime factors of 13725 and 13734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13725 and 13734.

How to find the GCF of 13725 and 13734?

We will first find the prime factorization of 13725 and 13734. After we will calculate the factors of 13725 and 13734 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 13734

Prime factors of 13734 are 2, 3, 7, 109. Prime factorization of 13734 in exponential form is:

13734 = 2¹ × 3² × 7¹ × 109¹

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 13734

List of positive integer factors of 13734 that divides 13725 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 109, 126, 218, 327, 654, 763, 981, 1526, 1962, 2289, 4578, 6867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13725 and 13734. The biggest common factor number is the GCF number.
So the greatest common factor 13725 and 13734 is 9.

Also check out the Least Common Multiple of 13725 and 13734