What is the Greatest Common Factor of 13940 and 13952?

Greatest common factor (GCF) of 13940 and 13952 is 4.

GCF(13940,13952) = 4

We will now calculate the prime factors of 13940 and 13952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13940 and 13952.

How to find the GCF of 13940 and 13952?

We will first find the prime factorization of 13940 and 13952. After we will calculate the factors of 13940 and 13952 and find the biggest common factor number .

Step-1: Prime Factorization of 13940

Prime factors of 13940 are 2, 5, 17, 41. Prime factorization of 13940 in exponential form is:

13940 = 2² × 5¹ × 17¹ × 41¹

Step-2: Prime Factorization of 13952

Prime factors of 13952 are 2, 109. Prime factorization of 13952 in exponential form is:

13952 = 2⁷ × 109¹

Step-3: Factors of 13940

List of positive integer factors of 13940 that divides 13940 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 41, 68, 82, 85, 164, 170, 205, 340, 410, 697, 820, 1394, 2788, 3485, 6970

Step-4: Factors of 13952

List of positive integer factors of 13952 that divides 13940 without a remainder.

1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 436, 872, 1744, 3488, 6976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13940 and 13952. The biggest common factor number is the GCF number.
So the greatest common factor 13940 and 13952 is 4.

Also check out the Least Common Multiple of 13940 and 13952