What is the Greatest Common Factor of 72960 and 72976?

Greatest common factor (GCF) of 72960 and 72976 is 16.

GCF(72960,72976) = 16

We will now calculate the prime factors of 72960 and 72976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72960 and 72976.

How to find the GCF of 72960 and 72976?

We will first find the prime factorization of 72960 and 72976. After we will calculate the factors of 72960 and 72976 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 72976

Prime factors of 72976 are 2, 4561. Prime factorization of 72976 in exponential form is:

72976 = 2⁴ × 4561¹

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 72976

List of positive integer factors of 72976 that divides 72960 without a remainder.

1, 2, 4, 8, 16, 4561, 9122, 18244, 36488

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72960 and 72976. The biggest common factor number is the GCF number.
So the greatest common factor 72960 and 72976 is 16.

Also check out the Least Common Multiple of 72960 and 72976