What is the Greatest Common Factor of 13900 and 13920?

Greatest common factor (GCF) of 13900 and 13920 is 20.

GCF(13900,13920) = 20

We will now calculate the prime factors of 13900 and 13920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13900 and 13920.

How to find the GCF of 13900 and 13920?

We will first find the prime factorization of 13900 and 13920. After we will calculate the factors of 13900 and 13920 and find the biggest common factor number .

Step-1: Prime Factorization of 13900

Prime factors of 13900 are 2, 5, 139. Prime factorization of 13900 in exponential form is:

13900 = 2² × 5² × 139¹

Step-2: Prime Factorization of 13920

Prime factors of 13920 are 2, 3, 5, 29. Prime factorization of 13920 in exponential form is:

13920 = 2⁵ × 3¹ × 5¹ × 29¹

Step-3: Factors of 13900

List of positive integer factors of 13900 that divides 13900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 139, 278, 556, 695, 1390, 2780, 3475, 6950

Step-4: Factors of 13920

List of positive integer factors of 13920 that divides 13900 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 80, 87, 96, 116, 120, 145, 160, 174, 232, 240, 290, 348, 435, 464, 480, 580, 696, 870, 928, 1160, 1392, 1740, 2320, 2784, 3480, 4640, 6960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13900 and 13920. The biggest common factor number is the GCF number.
So the greatest common factor 13900 and 13920 is 20.

Also check out the Least Common Multiple of 13900 and 13920