What is the Greatest Common Factor of 688 and 700?

Greatest common factor (GCF) of 688 and 700 is 4.

GCF(688,700) = 4

We will now calculate the prime factors of 688 and 700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 688 and 700.

How to find the GCF of 688 and 700?

We will first find the prime factorization of 688 and 700. After we will calculate the factors of 688 and 700 and find the biggest common factor number .

Step-1: Prime Factorization of 688

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

688 = 2⁴ × 43¹

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 688

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

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

Step-4: Factors of 700

List of positive integer factors of 700 that divides 688 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 688 and 700. The biggest common factor number is the GCF number.
So the greatest common factor 688 and 700 is 4.

Also check out the Least Common Multiple of 688 and 700