What is the Greatest Common Factor of 9975 and 9987?

Greatest common factor (GCF) of 9975 and 9987 is 3.

GCF(9975,9987) = 3

We will now calculate the prime factors of 9975 and 9987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9975 and 9987.

How to find the GCF of 9975 and 9987?

We will first find the prime factorization of 9975 and 9987. After we will calculate the factors of 9975 and 9987 and find the biggest common factor number .

Step-1: Prime Factorization of 9975

Prime factors of 9975 are 3, 5, 7, 19. Prime factorization of 9975 in exponential form is:

9975 = 3¹ × 5² × 7¹ × 19¹

Step-2: Prime Factorization of 9987

Prime factors of 9987 are 3, 3329. Prime factorization of 9987 in exponential form is:

9987 = 3¹ × 3329¹

Step-3: Factors of 9975

List of positive integer factors of 9975 that divides 9975 without a remainder.

1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325

Step-4: Factors of 9987

List of positive integer factors of 9987 that divides 9975 without a remainder.

1, 3, 3329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9975 and 9987. The biggest common factor number is the GCF number.
So the greatest common factor 9975 and 9987 is 3.

Also check out the Least Common Multiple of 9975 and 9987