What is the Greatest Common Factor of 675 and 688?

Greatest common factor (GCF) of 675 and 688 is 1.

GCF(675,688) = 1

We will now calculate the prime factors of 675 and 688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 675 and 688.

How to find the GCF of 675 and 688?

We will first find the prime factorization of 675 and 688. After we will calculate the factors of 675 and 688 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 688

Prime factors of 688 are 2, 43. Prime factorization of 688 in exponential form is:

688 = 2⁴ × 43¹

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 688

List of positive integer factors of 688 that divides 675 without a remainder.

1, 2, 4, 8, 16, 43, 86, 172, 344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 675 and 688. The biggest common factor number is the GCF number.
So the greatest common factor 675 and 688 is 1.

Also check out the Least Common Multiple of 675 and 688