What is the Greatest Common Factor of 67269 and 67275?

Greatest common factor (GCF) of 67269 and 67275 is 3.

GCF(67269,67275) = 3

We will now calculate the prime factors of 67269 and 67275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67269 and 67275.

How to find the GCF of 67269 and 67275?

We will first find the prime factorization of 67269 and 67275. After we will calculate the factors of 67269 and 67275 and find the biggest common factor number .

Step-1: Prime Factorization of 67269

Prime factors of 67269 are 3, 17, 1319. Prime factorization of 67269 in exponential form is:

67269 = 3¹ × 17¹ × 1319¹

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 67269

List of positive integer factors of 67269 that divides 67269 without a remainder.

1, 3, 17, 51, 1319, 3957, 22423

Step-4: Factors of 67275

List of positive integer factors of 67275 that divides 67269 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 67269 and 67275. The biggest common factor number is the GCF number.
So the greatest common factor 67269 and 67275 is 3.

Also check out the Least Common Multiple of 67269 and 67275