What is the Greatest Common Factor of 13965 and 13971?

Greatest common factor (GCF) of 13965 and 13971 is 3.

GCF(13965,13971) = 3

We will now calculate the prime factors of 13965 and 13971, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13965 and 13971.

How to find the GCF of 13965 and 13971?

We will first find the prime factorization of 13965 and 13971. After we will calculate the factors of 13965 and 13971 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 13971

Prime factors of 13971 are 3, 4657. Prime factorization of 13971 in exponential form is:

13971 = 3¹ × 4657¹

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 13971

List of positive integer factors of 13971 that divides 13965 without a remainder.

1, 3, 4657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13965 and 13971. The biggest common factor number is the GCF number.
So the greatest common factor 13965 and 13971 is 3.

Also check out the Least Common Multiple of 13965 and 13971