What is the Greatest Common Factor of 13700 and 13714?

Greatest common factor (GCF) of 13700 and 13714 is 2.

GCF(13700,13714) = 2

We will now calculate the prime factors of 13700 and 13714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13700 and 13714.

How to find the GCF of 13700 and 13714?

We will first find the prime factorization of 13700 and 13714. After we will calculate the factors of 13700 and 13714 and find the biggest common factor number .

Step-1: Prime Factorization of 13700

Prime factors of 13700 are 2, 5, 137. Prime factorization of 13700 in exponential form is:

13700 = 2² × 5² × 137¹

Step-2: Prime Factorization of 13714

Prime factors of 13714 are 2, 6857. Prime factorization of 13714 in exponential form is:

13714 = 2¹ × 6857¹

Step-3: Factors of 13700

List of positive integer factors of 13700 that divides 13700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 137, 274, 548, 685, 1370, 2740, 3425, 6850

Step-4: Factors of 13714

List of positive integer factors of 13714 that divides 13700 without a remainder.

1, 2, 6857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13700 and 13714. The biggest common factor number is the GCF number.
So the greatest common factor 13700 and 13714 is 2.

Also check out the Least Common Multiple of 13700 and 13714