What is the Greatest Common Factor of 13920 and 13938?

Greatest common factor (GCF) of 13920 and 13938 is 6.

GCF(13920,13938) = 6

We will now calculate the prime factors of 13920 and 13938, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13920 and 13938.

How to find the GCF of 13920 and 13938?

We will first find the prime factorization of 13920 and 13938. After we will calculate the factors of 13920 and 13938 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13938

Prime factors of 13938 are 2, 3, 23, 101. Prime factorization of 13938 in exponential form is:

13938 = 2¹ × 3¹ × 23¹ × 101¹

Step-3: Factors of 13920

List of positive integer factors of 13920 that divides 13920 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

Step-4: Factors of 13938

List of positive integer factors of 13938 that divides 13920 without a remainder.

1, 2, 3, 6, 23, 46, 69, 101, 138, 202, 303, 606, 2323, 4646, 6969

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13920 and 13938. The biggest common factor number is the GCF number.
So the greatest common factor 13920 and 13938 is 6.

Also check out the Least Common Multiple of 13920 and 13938