What is the Greatest Common Factor of 13974 and 13980?

Greatest common factor (GCF) of 13974 and 13980 is 6.

GCF(13974,13980) = 6

We will now calculate the prime factors of 13974 and 13980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13974 and 13980.

How to find the GCF of 13974 and 13980?

We will first find the prime factorization of 13974 and 13980. After we will calculate the factors of 13974 and 13980 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 13980

Prime factors of 13980 are 2, 3, 5, 233. Prime factorization of 13980 in exponential form is:

13980 = 2² × 3¹ × 5¹ × 233¹

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 13980

List of positive integer factors of 13980 that divides 13974 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 233, 466, 699, 932, 1165, 1398, 2330, 2796, 3495, 4660, 6990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13974 and 13980. The biggest common factor number is the GCF number.
So the greatest common factor 13974 and 13980 is 6.

Also check out the Least Common Multiple of 13974 and 13980