What is the Greatest Common Factor of 67260 and 67275?

Greatest common factor (GCF) of 67260 and 67275 is 15.

GCF(67260,67275) = 15

We will now calculate the prime factors of 67260 and 67275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67260 and 67275.

How to find the GCF of 67260 and 67275?

We will first find the prime factorization of 67260 and 67275. After we will calculate the factors of 67260 and 67275 and find the biggest common factor number .

Step-1: Prime Factorization of 67260

Prime factors of 67260 are 2, 3, 5, 19, 59. Prime factorization of 67260 in exponential form is:

67260 = 2² × 3¹ × 5¹ × 19¹ × 59¹

Step-2: Prime Factorization of 67275

Prime factors of 67275 are 3, 5, 13, 23. Prime factorization of 67275 in exponential form is:

67275 = 3² × 5² × 13¹ × 23¹

Step-3: Factors of 67260

List of positive integer factors of 67260 that divides 67260 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 59, 60, 76, 95, 114, 118, 177, 190, 228, 236, 285, 295, 354, 380, 570, 590, 708, 885, 1121, 1140, 1180, 1770, 2242, 3363, 3540, 4484, 5605, 6726, 11210, 13452, 16815, 22420, 33630

Step-4: Factors of 67275

List of positive integer factors of 67275 that divides 67260 without a remainder.

1, 3, 5, 9, 13, 15, 23, 25, 39, 45, 65, 69, 75, 115, 117, 195, 207, 225, 299, 325, 345, 575, 585, 897, 975, 1035, 1495, 1725, 2691, 2925, 4485, 5175, 7475, 13455, 22425

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67260 and 67275. The biggest common factor number is the GCF number.
So the greatest common factor 67260 and 67275 is 15.

Also check out the Least Common Multiple of 67260 and 67275