What is the Greatest Common Factor of 13974 and 13987?

Greatest common factor (GCF) of 13974 and 13987 is 1.

GCF(13974,13987) = 1

We will now calculate the prime factors of 13974 and 13987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13974 and 13987.

How to find the GCF of 13974 and 13987?

We will first find the prime factorization of 13974 and 13987. After we will calculate the factors of 13974 and 13987 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 13987

Prime factors of 13987 are 71, 197. Prime factorization of 13987 in exponential form is:

13987 = 71¹ × 197¹

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 13987

List of positive integer factors of 13987 that divides 13974 without a remainder.

1, 71, 197

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13974 and 13987. The biggest common factor number is the GCF number.
So the greatest common factor 13974 and 13987 is 1.

Also check out the Least Common Multiple of 13974 and 13987