What is the Greatest Common Factor of 700 and 714?

Greatest common factor (GCF) of 700 and 714 is 14.

GCF(700,714) = 14

We will now calculate the prime factors of 700 and 714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 700 and 714.

How to find the GCF of 700 and 714?

We will first find the prime factorization of 700 and 714. After we will calculate the factors of 700 and 714 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 714

Prime factors of 714 are 2, 3, 7, 17. Prime factorization of 714 in exponential form is:

714 = 2¹ × 3¹ × 7¹ × 17¹

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 714

List of positive integer factors of 714 that divides 700 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 700 and 714. The biggest common factor number is the GCF number.
So the greatest common factor 700 and 714 is 14.

Also check out the Least Common Multiple of 700 and 714