What is the Greatest Common Factor of 675 and 680?

Greatest common factor (GCF) of 675 and 680 is 5.

GCF(675,680) = 5

We will now calculate the prime factors of 675 and 680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 675 and 680.

How to find the GCF of 675 and 680?

We will first find the prime factorization of 675 and 680. After we will calculate the factors of 675 and 680 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 680

Prime factors of 680 are 2, 5, 17. Prime factorization of 680 in exponential form is:

680 = 2³ × 5¹ × 17¹

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 680

List of positive integer factors of 680 that divides 675 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 675 and 680. The biggest common factor number is the GCF number.
So the greatest common factor 675 and 680 is 5.

Also check out the Least Common Multiple of 675 and 680