What is the Greatest Common Factor of 3975 and 3990?

Greatest common factor (GCF) of 3975 and 3990 is 15.

GCF(3975,3990) = 15

We will now calculate the prime factors of 3975 and 3990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3975 and 3990.

How to find the GCF of 3975 and 3990?

We will first find the prime factorization of 3975 and 3990. After we will calculate the factors of 3975 and 3990 and find the biggest common factor number .

Step-1: Prime Factorization of 3975

Prime factors of 3975 are 3, 5, 53. Prime factorization of 3975 in exponential form is:

3975 = 3¹ × 5² × 53¹

Step-2: Prime Factorization of 3990

Prime factors of 3990 are 2, 3, 5, 7, 19. Prime factorization of 3990 in exponential form is:

3990 = 2¹ × 3¹ × 5¹ × 7¹ × 19¹

Step-3: Factors of 3975

List of positive integer factors of 3975 that divides 3975 without a remainder.

1, 3, 5, 15, 25, 53, 75, 159, 265, 795, 1325

Step-4: Factors of 3990

List of positive integer factors of 3990 that divides 3975 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 30, 35, 38, 42, 57, 70, 95, 105, 114, 133, 190, 210, 266, 285, 399, 570, 665, 798, 1330, 1995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3975 and 3990. The biggest common factor number is the GCF number.
So the greatest common factor 3975 and 3990 is 15.

Also check out the Least Common Multiple of 3975 and 3990