What is the Greatest Common Factor of 39975 and 39988?

Greatest common factor (GCF) of 39975 and 39988 is 13.

GCF(39975,39988) = 13

We will now calculate the prime factors of 39975 and 39988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39975 and 39988.

How to find the GCF of 39975 and 39988?

We will first find the prime factorization of 39975 and 39988. After we will calculate the factors of 39975 and 39988 and find the biggest common factor number .

Step-1: Prime Factorization of 39975

Prime factors of 39975 are 3, 5, 13, 41. Prime factorization of 39975 in exponential form is:

39975 = 3¹ × 5² × 13¹ × 41¹

Step-2: Prime Factorization of 39988

Prime factors of 39988 are 2, 13, 769. Prime factorization of 39988 in exponential form is:

39988 = 2² × 13¹ × 769¹

Step-3: Factors of 39975

List of positive integer factors of 39975 that divides 39975 without a remainder.

1, 3, 5, 13, 15, 25, 39, 41, 65, 75, 123, 195, 205, 325, 533, 615, 975, 1025, 1599, 2665, 3075, 7995, 13325

Step-4: Factors of 39988

List of positive integer factors of 39988 that divides 39975 without a remainder.

1, 2, 4, 13, 26, 52, 769, 1538, 3076, 9997, 19994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39975 and 39988. The biggest common factor number is the GCF number.
So the greatest common factor 39975 and 39988 is 13.

Also check out the Least Common Multiple of 39975 and 39988