What is the Greatest Common Factor of 72960 and 72980?

Greatest common factor (GCF) of 72960 and 72980 is 20.

GCF(72960,72980) = 20

We will now calculate the prime factors of 72960 and 72980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72960 and 72980.

How to find the GCF of 72960 and 72980?

We will first find the prime factorization of 72960 and 72980. After we will calculate the factors of 72960 and 72980 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 72980

Prime factors of 72980 are 2, 5, 41, 89. Prime factorization of 72980 in exponential form is:

72980 = 2² × 5¹ × 41¹ × 89¹

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 72980

List of positive integer factors of 72980 that divides 72960 without a remainder.

1, 2, 4, 5, 10, 20, 41, 82, 89, 164, 178, 205, 356, 410, 445, 820, 890, 1780, 3649, 7298, 14596, 18245, 36490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72960 and 72980. The biggest common factor number is the GCF number.
So the greatest common factor 72960 and 72980 is 20.

Also check out the Least Common Multiple of 72960 and 72980