What is the Greatest Common Factor of 686 and 700?

Greatest common factor (GCF) of 686 and 700 is 14.

GCF(686,700) = 14

We will now calculate the prime factors of 686 and 700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 686 and 700.

How to find the GCF of 686 and 700?

We will first find the prime factorization of 686 and 700. After we will calculate the factors of 686 and 700 and find the biggest common factor number .

Step-1: Prime Factorization of 686

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

686 = 2¹ × 7³

Step-2: Prime Factorization of 700

Prime factors of 700 are 2, 5, 7. Prime factorization of 700 in exponential form is:

700 = 2² × 5² × 7¹

Step-3: Factors of 686

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

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

Step-4: Factors of 700

List of positive integer factors of 700 that divides 686 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 686 and 700. The biggest common factor number is the GCF number.
So the greatest common factor 686 and 700 is 14.

Also check out the Least Common Multiple of 686 and 700