What is the Greatest Common Factor of 9960 and 9972?

Greatest common factor (GCF) of 9960 and 9972 is 12.

GCF(9960,9972) = 12

We will now calculate the prime factors of 9960 and 9972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9960 and 9972.

How to find the GCF of 9960 and 9972?

We will first find the prime factorization of 9960 and 9972. After we will calculate the factors of 9960 and 9972 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 9972

Prime factors of 9972 are 2, 3, 277. Prime factorization of 9972 in exponential form is:

9972 = 2² × 3² × 277¹

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 9972

List of positive integer factors of 9972 that divides 9960 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9960 and 9972. The biggest common factor number is the GCF number.
So the greatest common factor 9960 and 9972 is 12.

Also check out the Least Common Multiple of 9960 and 9972