What is the Greatest Common Factor of 13965 and 13985?

Greatest common factor (GCF) of 13965 and 13985 is 5.

GCF(13965,13985) = 5

We will now calculate the prime factors of 13965 and 13985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13965 and 13985.

How to find the GCF of 13965 and 13985?

We will first find the prime factorization of 13965 and 13985. After we will calculate the factors of 13965 and 13985 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 13985

Prime factors of 13985 are 5, 2797. Prime factorization of 13985 in exponential form is:

13985 = 5¹ × 2797¹

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 13985

List of positive integer factors of 13985 that divides 13965 without a remainder.

1, 5, 2797

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13965 and 13985. The biggest common factor number is the GCF number.
So the greatest common factor 13965 and 13985 is 5.

Also check out the Least Common Multiple of 13965 and 13985