What is the Greatest Common Factor of 675 and 687?

Greatest common factor (GCF) of 675 and 687 is 3.

GCF(675,687) = 3

We will now calculate the prime factors of 675 and 687, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 675 and 687.

How to find the GCF of 675 and 687?

We will first find the prime factorization of 675 and 687. After we will calculate the factors of 675 and 687 and find the biggest common factor number .

Step-1: Prime Factorization of 675

Prime factors of 675 are 3, 5. Prime factorization of 675 in exponential form is:

675 = 3³ × 5²

Step-2: Prime Factorization of 687

Prime factors of 687 are 3, 229. Prime factorization of 687 in exponential form is:

687 = 3¹ × 229¹

Step-3: Factors of 675

List of positive integer factors of 675 that divides 675 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225

Step-4: Factors of 687

List of positive integer factors of 687 that divides 675 without a remainder.

1, 3, 229

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 675 and 687. The biggest common factor number is the GCF number.
So the greatest common factor 675 and 687 is 3.

Also check out the Least Common Multiple of 675 and 687