What is the Greatest Common Factor of 13725 and 13744?

Greatest common factor (GCF) of 13725 and 13744 is 1.

GCF(13725,13744) = 1

We will now calculate the prime factors of 13725 and 13744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13725 and 13744.

How to find the GCF of 13725 and 13744?

We will first find the prime factorization of 13725 and 13744. After we will calculate the factors of 13725 and 13744 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 13744

Prime factors of 13744 are 2, 859. Prime factorization of 13744 in exponential form is:

13744 = 2⁴ × 859¹

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 13744

List of positive integer factors of 13744 that divides 13725 without a remainder.

1, 2, 4, 8, 16, 859, 1718, 3436, 6872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13725 and 13744. The biggest common factor number is the GCF number.
So the greatest common factor 13725 and 13744 is 1.

Also check out the Least Common Multiple of 13725 and 13744