What is the Greatest Common Factor of 9975 and 9980?

Greatest common factor (GCF) of 9975 and 9980 is 5.

GCF(9975,9980) = 5

We will now calculate the prime factors of 9975 and 9980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9975 and 9980.

How to find the GCF of 9975 and 9980?

We will first find the prime factorization of 9975 and 9980. After we will calculate the factors of 9975 and 9980 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 9980

Prime factors of 9980 are 2, 5, 499. Prime factorization of 9980 in exponential form is:

9980 = 2² × 5¹ × 499¹

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 9980

List of positive integer factors of 9980 that divides 9975 without a remainder.

1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9975 and 9980. The biggest common factor number is the GCF number.
So the greatest common factor 9975 and 9980 is 5.

Also check out the Least Common Multiple of 9975 and 9980