What is the Greatest Common Factor of 72960 and 72975?

Greatest common factor (GCF) of 72960 and 72975 is 15.

GCF(72960,72975) = 15

We will now calculate the prime factors of 72960 and 72975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72960 and 72975.

How to find the GCF of 72960 and 72975?

We will first find the prime factorization of 72960 and 72975. After we will calculate the factors of 72960 and 72975 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 72975

Prime factors of 72975 are 3, 5, 7, 139. Prime factorization of 72975 in exponential form is:

72975 = 3¹ × 5² × 7¹ × 139¹

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 72975

List of positive integer factors of 72975 that divides 72960 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 139, 175, 417, 525, 695, 973, 2085, 2919, 3475, 4865, 10425, 14595, 24325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72960 and 72975. The biggest common factor number is the GCF number.
So the greatest common factor 72960 and 72975 is 15.

Also check out the Least Common Multiple of 72960 and 72975