What is the Greatest Common Factor of 9960 and 9975?

Greatest common factor (GCF) of 9960 and 9975 is 15.

GCF(9960,9975) = 15

We will now calculate the prime factors of 9960 and 9975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9960 and 9975.

How to find the GCF of 9960 and 9975?

We will first find the prime factorization of 9960 and 9975. After we will calculate the factors of 9960 and 9975 and find the biggest common factor number .

Step-1: Prime Factorization of 9960

Prime factors of 9960 are 2, 3, 5, 83. Prime factorization of 9960 in exponential form is:

9960 = 2³ × 3¹ × 5¹ × 83¹

Step-2: 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-3: Factors of 9960

List of positive integer factors of 9960 that divides 9960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980

Step-4: Factors of 9975

List of positive integer factors of 9975 that divides 9960 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9960 and 9975. The biggest common factor number is the GCF number.
So the greatest common factor 9960 and 9975 is 15.

Also check out the Least Common Multiple of 9960 and 9975