What is the Greatest Common Factor of 13706 and 13720?

Greatest common factor (GCF) of 13706 and 13720 is 14.

GCF(13706,13720) = 14

We will now calculate the prime factors of 13706 and 13720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13706 and 13720.

How to find the GCF of 13706 and 13720?

We will first find the prime factorization of 13706 and 13720. After we will calculate the factors of 13706 and 13720 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13720

Prime factors of 13720 are 2, 5, 7. Prime factorization of 13720 in exponential form is:

13720 = 2³ × 5¹ × 7³

Step-3: Factors of 13706

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

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

Step-4: Factors of 13720

List of positive integer factors of 13720 that divides 13706 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 343, 392, 490, 686, 980, 1372, 1715, 1960, 2744, 3430, 6860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13706 and 13720. The biggest common factor number is the GCF number.
So the greatest common factor 13706 and 13720 is 14.

Also check out the Least Common Multiple of 13706 and 13720