What is the Greatest Common Factor of 67275 and 67280?

Greatest common factor (GCF) of 67275 and 67280 is 5.

GCF(67275,67280) = 5

We will now calculate the prime factors of 67275 and 67280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67275 and 67280.

How to find the GCF of 67275 and 67280?

We will first find the prime factorization of 67275 and 67280. After we will calculate the factors of 67275 and 67280 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67280

Prime factors of 67280 are 2, 5, 29. Prime factorization of 67280 in exponential form is:

67280 = 2⁴ × 5¹ × 29²

Step-3: Factors of 67275

List of positive integer factors of 67275 that divides 67275 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

Step-4: Factors of 67280

List of positive integer factors of 67280 that divides 67275 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, 841, 1160, 1682, 2320, 3364, 4205, 6728, 8410, 13456, 16820, 33640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67275 and 67280. The biggest common factor number is the GCF number.
So the greatest common factor 67275 and 67280 is 5.

Also check out the Least Common Multiple of 67275 and 67280