What is the Greatest Common Factor of 72945 and 72960?

Greatest common factor (GCF) of 72945 and 72960 is 15.

GCF(72945,72960) = 15

We will now calculate the prime factors of 72945 and 72960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72945 and 72960.

How to find the GCF of 72945 and 72960?

We will first find the prime factorization of 72945 and 72960. After we will calculate the factors of 72945 and 72960 and find the biggest common factor number .

Step-1: Prime Factorization of 72945

Prime factors of 72945 are 3, 5, 1621. Prime factorization of 72945 in exponential form is:

72945 = 3² × 5¹ × 1621¹

Step-2: 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-3: Factors of 72945

List of positive integer factors of 72945 that divides 72945 without a remainder.

1, 3, 5, 9, 15, 45, 1621, 4863, 8105, 14589, 24315

Step-4: Factors of 72960

List of positive integer factors of 72960 that divides 72945 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72945 and 72960. The biggest common factor number is the GCF number.
So the greatest common factor 72945 and 72960 is 15.

Also check out the Least Common Multiple of 72945 and 72960