What is the Greatest Common Factor of 13965 and 13972?

Greatest common factor (GCF) of 13965 and 13972 is 7.

GCF(13965,13972) = 7

We will now calculate the prime factors of 13965 and 13972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13965 and 13972.

How to find the GCF of 13965 and 13972?

We will first find the prime factorization of 13965 and 13972. After we will calculate the factors of 13965 and 13972 and find the biggest common factor number .

Step-1: Prime Factorization of 13965

Prime factors of 13965 are 3, 5, 7, 19. Prime factorization of 13965 in exponential form is:

13965 = 3¹ × 5¹ × 7² × 19¹

Step-2: Prime Factorization of 13972

Prime factors of 13972 are 2, 7, 499. Prime factorization of 13972 in exponential form is:

13972 = 2² × 7¹ × 499¹

Step-3: Factors of 13965

List of positive integer factors of 13965 that divides 13965 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655

Step-4: Factors of 13972

List of positive integer factors of 13972 that divides 13965 without a remainder.

1, 2, 4, 7, 14, 28, 499, 998, 1996, 3493, 6986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13965 and 13972. The biggest common factor number is the GCF number.
So the greatest common factor 13965 and 13972 is 7.

Also check out the Least Common Multiple of 13965 and 13972