What is the Greatest Common Factor of 39975 and 39980?

Greatest common factor (GCF) of 39975 and 39980 is 5.

GCF(39975,39980) = 5

We will now calculate the prime factors of 39975 and 39980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39975 and 39980.

How to find the GCF of 39975 and 39980?

We will first find the prime factorization of 39975 and 39980. After we will calculate the factors of 39975 and 39980 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 39980

Prime factors of 39980 are 2, 5, 1999. Prime factorization of 39980 in exponential form is:

39980 = 2² × 5¹ × 1999¹

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 39980

List of positive integer factors of 39980 that divides 39975 without a remainder.

1, 2, 4, 5, 10, 20, 1999, 3998, 7996, 9995, 19990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39975 and 39980. The biggest common factor number is the GCF number.
So the greatest common factor 39975 and 39980 is 5.

Also check out the Least Common Multiple of 39975 and 39980