What is the Greatest Common Factor of 39964 and 39975?

Greatest common factor (GCF) of 39964 and 39975 is 1.

GCF(39964,39975) = 1

We will now calculate the prime factors of 39964 and 39975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39964 and 39975.

How to find the GCF of 39964 and 39975?

We will first find the prime factorization of 39964 and 39975. After we will calculate the factors of 39964 and 39975 and find the biggest common factor number .

Step-1: Prime Factorization of 39964

Prime factors of 39964 are 2, 97, 103. Prime factorization of 39964 in exponential form is:

39964 = 2² × 97¹ × 103¹

Step-2: 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-3: Factors of 39964

List of positive integer factors of 39964 that divides 39964 without a remainder.

1, 2, 4, 97, 103, 194, 206, 388, 412, 9991, 19982

Step-4: Factors of 39975

List of positive integer factors of 39975 that divides 39964 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39964 and 39975. The biggest common factor number is the GCF number.
So the greatest common factor 39964 and 39975 is 1.

Also check out the Least Common Multiple of 39964 and 39975