What is the Greatest Common Factor of 700 and 706?

Greatest common factor (GCF) of 700 and 706 is 2.

GCF(700,706) = 2

We will now calculate the prime factors of 700 and 706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 700 and 706.

How to find the GCF of 700 and 706?

We will first find the prime factorization of 700 and 706. After we will calculate the factors of 700 and 706 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 706

Prime factors of 706 are 2, 353. Prime factorization of 706 in exponential form is:

706 = 2¹ × 353¹

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 706

List of positive integer factors of 706 that divides 700 without a remainder.

1, 2, 353

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 700 and 706. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 706 is 2.

Also check out the Least Common Multiple of 700 and 706