What is the Greatest Common Factor of 75285 and 75300?

Greatest common factor (GCF) of 75285 and 75300 is 15.

GCF(75285,75300) = 15

We will now calculate the prime factors of 75285 and 75300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75285 and 75300.

How to find the GCF of 75285 and 75300?

We will first find the prime factorization of 75285 and 75300. After we will calculate the factors of 75285 and 75300 and find the biggest common factor number .

Step-1: Prime Factorization of 75285

Prime factors of 75285 are 3, 5, 7, 239. Prime factorization of 75285 in exponential form is:

75285 = 3² × 5¹ × 7¹ × 239¹

Step-2: Prime Factorization of 75300

Prime factors of 75300 are 2, 3, 5, 251. Prime factorization of 75300 in exponential form is:

75300 = 2² × 3¹ × 5² × 251¹

Step-3: Factors of 75285

List of positive integer factors of 75285 that divides 75285 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 239, 315, 717, 1195, 1673, 2151, 3585, 5019, 8365, 10755, 15057, 25095

Step-4: Factors of 75300

List of positive integer factors of 75300 that divides 75285 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 251, 300, 502, 753, 1004, 1255, 1506, 2510, 3012, 3765, 5020, 6275, 7530, 12550, 15060, 18825, 25100, 37650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75285 and 75300. The biggest common factor number is the GCF number.
So the greatest common factor 75285 and 75300 is 15.

Also check out the Least Common Multiple of 75285 and 75300