What is the Greatest Common Factor of 13974 and 13991?

Greatest common factor (GCF) of 13974 and 13991 is 17.

GCF(13974,13991) = 17

We will now calculate the prime factors of 13974 and 13991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13974 and 13991.

How to find the GCF of 13974 and 13991?

We will first find the prime factorization of 13974 and 13991. After we will calculate the factors of 13974 and 13991 and find the biggest common factor number .

Step-1: Prime Factorization of 13974

Prime factors of 13974 are 2, 3, 17, 137. Prime factorization of 13974 in exponential form is:

13974 = 2¹ × 3¹ × 17¹ × 137¹

Step-2: Prime Factorization of 13991

Prime factors of 13991 are 17, 823. Prime factorization of 13991 in exponential form is:

13991 = 17¹ × 823¹

Step-3: Factors of 13974

List of positive integer factors of 13974 that divides 13974 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 137, 274, 411, 822, 2329, 4658, 6987

Step-4: Factors of 13991

List of positive integer factors of 13991 that divides 13974 without a remainder.

1, 17, 823

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13974 and 13991. The biggest common factor number is the GCF number.
So the greatest common factor 13974 and 13991 is 17.

Also check out the Least Common Multiple of 13974 and 13991