What is the Greatest Common Factor of 13954 and 13974?

Greatest common factor (GCF) of 13954 and 13974 is 2.

GCF(13954,13974) = 2

We will now calculate the prime factors of 13954 and 13974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13954 and 13974.

How to find the GCF of 13954 and 13974?

We will first find the prime factorization of 13954 and 13974. After we will calculate the factors of 13954 and 13974 and find the biggest common factor number .

Step-1: Prime Factorization of 13954

Prime factors of 13954 are 2, 6977. Prime factorization of 13954 in exponential form is:

13954 = 2¹ × 6977¹

Step-2: 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-3: Factors of 13954

List of positive integer factors of 13954 that divides 13954 without a remainder.

1, 2, 6977

Step-4: Factors of 13974

List of positive integer factors of 13974 that divides 13954 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13954 and 13974. The biggest common factor number is the GCF number.
So the greatest common factor 13954 and 13974 is 2.

Also check out the Least Common Multiple of 13954 and 13974