What is the Greatest Common Factor of 672 and 686?

Greatest common factor (GCF) of 672 and 686 is 14.

GCF(672,686) = 14

We will now calculate the prime factors of 672 and 686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 672 and 686.

How to find the GCF of 672 and 686?

We will first find the prime factorization of 672 and 686. After we will calculate the factors of 672 and 686 and find the biggest common factor number .

Step-1: Prime Factorization of 672

Prime factors of 672 are 2, 3, 7. Prime factorization of 672 in exponential form is:

672 = 2⁵ × 3¹ × 7¹

Step-2: Prime Factorization of 686

Prime factors of 686 are 2, 7. Prime factorization of 686 in exponential form is:

686 = 2¹ × 7³

Step-3: Factors of 672

List of positive integer factors of 672 that divides 672 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336

Step-4: Factors of 686

List of positive integer factors of 686 that divides 672 without a remainder.

1, 2, 7, 14, 49, 98, 343

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 672 and 686. The biggest common factor number is the GCF number.
So the greatest common factor 672 and 686 is 14.

Also check out the Least Common Multiple of 672 and 686