What is the Greatest Common Factor of 700 and 707?

Greatest common factor (GCF) of 700 and 707 is 7.

GCF(700,707) = 7

We will now calculate the prime factors of 700 and 707, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 700 and 707.

How to find the GCF of 700 and 707?

We will first find the prime factorization of 700 and 707. After we will calculate the factors of 700 and 707 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 707

Prime factors of 707 are 7, 101. Prime factorization of 707 in exponential form is:

707 = 7¹ × 101¹

Step-3: Factors of 700

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

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

Step-4: Factors of 707

List of positive integer factors of 707 that divides 700 without a remainder.

1, 7, 101

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 700 and 707. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 707 is 7.

Also check out the Least Common Multiple of 700 and 707