What is the Greatest Common Factor of 700 and 709?

Greatest common factor (GCF) of 700 and 709 is 1.

GCF(700,709) = 1

We will now calculate the prime factors of 700 and 709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 700 and 709.

How to find the GCF of 700 and 709?

We will first find the prime factorization of 700 and 709. After we will calculate the factors of 700 and 709 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 709

Prime factors of 709 are 709. Prime factorization of 709 in exponential form is:

709 = 709¹

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 709

List of positive integer factors of 709 that divides 700 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 700 and 709. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 709 is 1.

Also check out the Least Common Multiple of 700 and 709