What is the Greatest Common Factor of 13974 and 13984?

Greatest common factor (GCF) of 13974 and 13984 is 2.

GCF(13974,13984) = 2

We will now calculate the prime factors of 13974 and 13984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13974 and 13984.

How to find the GCF of 13974 and 13984?

We will first find the prime factorization of 13974 and 13984. After we will calculate the factors of 13974 and 13984 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 13984

Prime factors of 13984 are 2, 19, 23. Prime factorization of 13984 in exponential form is:

13984 = 2⁵ × 19¹ × 23¹

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 13984

List of positive integer factors of 13984 that divides 13974 without a remainder.

1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 76, 92, 152, 184, 304, 368, 437, 608, 736, 874, 1748, 3496, 6992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13974 and 13984. The biggest common factor number is the GCF number.
So the greatest common factor 13974 and 13984 is 2.

Also check out the Least Common Multiple of 13974 and 13984