What is the Greatest Common Factor of 75270 and 75285?

Greatest common factor (GCF) of 75270 and 75285 is 15.

GCF(75270,75285) = 15

We will now calculate the prime factors of 75270 and 75285, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75270 and 75285.

How to find the GCF of 75270 and 75285?

We will first find the prime factorization of 75270 and 75285. After we will calculate the factors of 75270 and 75285 and find the biggest common factor number .

Step-1: Prime Factorization of 75270

Prime factors of 75270 are 2, 3, 5, 13, 193. Prime factorization of 75270 in exponential form is:

75270 = 2¹ × 3¹ × 5¹ × 13¹ × 193¹

Step-2: 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-3: Factors of 75270

List of positive integer factors of 75270 that divides 75270 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 193, 195, 386, 390, 579, 965, 1158, 1930, 2509, 2895, 5018, 5790, 7527, 12545, 15054, 25090, 37635

Step-4: Factors of 75285

List of positive integer factors of 75285 that divides 75270 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75270 and 75285. The biggest common factor number is the GCF number.
So the greatest common factor 75270 and 75285 is 15.

Also check out the Least Common Multiple of 75270 and 75285