What is the Greatest Common Factor of 13700 and 13706?

Greatest common factor (GCF) of 13700 and 13706 is 2.

GCF(13700,13706) = 2

We will now calculate the prime factors of 13700 and 13706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13700 and 13706.

How to find the GCF of 13700 and 13706?

We will first find the prime factorization of 13700 and 13706. After we will calculate the factors of 13700 and 13706 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 13706

Prime factors of 13706 are 2, 7, 11, 89. Prime factorization of 13706 in exponential form is:

13706 = 2¹ × 7¹ × 11¹ × 89¹

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 13706

List of positive integer factors of 13706 that divides 13700 without a remainder.

1, 2, 7, 11, 14, 22, 77, 89, 154, 178, 623, 979, 1246, 1958, 6853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13700 and 13706. The biggest common factor number is the GCF number.
So the greatest common factor 13700 and 13706 is 2.

Also check out the Least Common Multiple of 13700 and 13706