What is the Greatest Common Factor of 72660 and 72675?

Greatest common factor (GCF) of 72660 and 72675 is 15.

GCF(72660,72675) = 15

We will now calculate the prime factors of 72660 and 72675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72660 and 72675.

How to find the GCF of 72660 and 72675?

We will first find the prime factorization of 72660 and 72675. After we will calculate the factors of 72660 and 72675 and find the biggest common factor number .

Step-1: Prime Factorization of 72660

Prime factors of 72660 are 2, 3, 5, 7, 173. Prime factorization of 72660 in exponential form is:

72660 = 2² × 3¹ × 5¹ × 7¹ × 173¹

Step-2: Prime Factorization of 72675

Prime factors of 72675 are 3, 5, 17, 19. Prime factorization of 72675 in exponential form is:

72675 = 3² × 5² × 17¹ × 19¹

Step-3: Factors of 72660

List of positive integer factors of 72660 that divides 72660 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 173, 210, 346, 420, 519, 692, 865, 1038, 1211, 1730, 2076, 2422, 2595, 3460, 3633, 4844, 5190, 6055, 7266, 10380, 12110, 14532, 18165, 24220, 36330

Step-4: Factors of 72675

List of positive integer factors of 72675 that divides 72660 without a remainder.

1, 3, 5, 9, 15, 17, 19, 25, 45, 51, 57, 75, 85, 95, 153, 171, 225, 255, 285, 323, 425, 475, 765, 855, 969, 1275, 1425, 1615, 2907, 3825, 4275, 4845, 8075, 14535, 24225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72660 and 72675. The biggest common factor number is the GCF number.
So the greatest common factor 72660 and 72675 is 15.

Also check out the Least Common Multiple of 72660 and 72675