What is the Greatest Common Factor of 72658 and 72675?

Greatest common factor (GCF) of 72658 and 72675 is 17.

GCF(72658,72675) = 17

We will now calculate the prime factors of 72658 and 72675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72658 and 72675.

How to find the GCF of 72658 and 72675?

We will first find the prime factorization of 72658 and 72675. After we will calculate the factors of 72658 and 72675 and find the biggest common factor number .

Step-1: Prime Factorization of 72658

Prime factors of 72658 are 2, 17, 2137. Prime factorization of 72658 in exponential form is:

72658 = 2¹ × 17¹ × 2137¹

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 72658

List of positive integer factors of 72658 that divides 72658 without a remainder.

1, 2, 17, 34, 2137, 4274, 36329

Step-4: Factors of 72675

List of positive integer factors of 72675 that divides 72658 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 72658 and 72675. The biggest common factor number is the GCF number.
So the greatest common factor 72658 and 72675 is 17.

Also check out the Least Common Multiple of 72658 and 72675