What is the Greatest Common Factor of 13725 and 13738?

Greatest common factor (GCF) of 13725 and 13738 is 1.

GCF(13725,13738) = 1

We will now calculate the prime factors of 13725 and 13738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13725 and 13738.

How to find the GCF of 13725 and 13738?

We will first find the prime factorization of 13725 and 13738. After we will calculate the factors of 13725 and 13738 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 13738

Prime factors of 13738 are 2, 6869. Prime factorization of 13738 in exponential form is:

13738 = 2¹ × 6869¹

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 13738

List of positive integer factors of 13738 that divides 13725 without a remainder.

1, 2, 6869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13725 and 13738. The biggest common factor number is the GCF number.
So the greatest common factor 13725 and 13738 is 1.

Also check out the Least Common Multiple of 13725 and 13738