What is the Greatest Common Factor of 72960 and 72972?

Greatest common factor (GCF) of 72960 and 72972 is 12.

GCF(72960,72972) = 12

We will now calculate the prime factors of 72960 and 72972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72960 and 72972.

How to find the GCF of 72960 and 72972?

We will first find the prime factorization of 72960 and 72972. After we will calculate the factors of 72960 and 72972 and find the biggest common factor number .

Step-1: Prime Factorization of 72960

Prime factors of 72960 are 2, 3, 5, 19. Prime factorization of 72960 in exponential form is:

72960 = 2⁸ × 3¹ × 5¹ × 19¹

Step-2: Prime Factorization of 72972

Prime factors of 72972 are 2, 3, 2027. Prime factorization of 72972 in exponential form is:

72972 = 2² × 3² × 2027¹

Step-3: Factors of 72960

List of positive integer factors of 72960 that divides 72960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 64, 76, 80, 95, 96, 114, 120, 128, 152, 160, 190, 192, 228, 240, 256, 285, 304, 320, 380, 384, 456, 480, 570, 608, 640, 760, 768, 912, 960, 1140, 1216, 1280, 1520, 1824, 1920, 2280, 2432, 3040, 3648, 3840, 4560, 4864, 6080, 7296, 9120, 12160, 14592, 18240, 24320, 36480

Step-4: Factors of 72972

List of positive integer factors of 72972 that divides 72960 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2027, 4054, 6081, 8108, 12162, 18243, 24324, 36486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72960 and 72972. The biggest common factor number is the GCF number.
So the greatest common factor 72960 and 72972 is 12.

Also check out the Least Common Multiple of 72960 and 72972