What is the Greatest Common Factor of 13975 and 13982?

Greatest common factor (GCF) of 13975 and 13982 is 1.

GCF(13975,13982) = 1

We will now calculate the prime factors of 13975 and 13982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13975 and 13982.

How to find the GCF of 13975 and 13982?

We will first find the prime factorization of 13975 and 13982. After we will calculate the factors of 13975 and 13982 and find the biggest common factor number .

Step-1: Prime Factorization of 13975

Prime factors of 13975 are 5, 13, 43. Prime factorization of 13975 in exponential form is:

13975 = 5² × 13¹ × 43¹

Step-2: Prime Factorization of 13982

Prime factors of 13982 are 2, 6991. Prime factorization of 13982 in exponential form is:

13982 = 2¹ × 6991¹

Step-3: Factors of 13975

List of positive integer factors of 13975 that divides 13975 without a remainder.

1, 5, 13, 25, 43, 65, 215, 325, 559, 1075, 2795

Step-4: Factors of 13982

List of positive integer factors of 13982 that divides 13975 without a remainder.

1, 2, 6991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13975 and 13982. The biggest common factor number is the GCF number.
So the greatest common factor 13975 and 13982 is 1.

Also check out the Least Common Multiple of 13975 and 13982