What is the Greatest Common Factor of 13940 and 13954?

Greatest common factor (GCF) of 13940 and 13954 is 2.

GCF(13940,13954) = 2

We will now calculate the prime factors of 13940 and 13954, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13940 and 13954.

How to find the GCF of 13940 and 13954?

We will first find the prime factorization of 13940 and 13954. After we will calculate the factors of 13940 and 13954 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 13954

Prime factors of 13954 are 2, 6977. Prime factorization of 13954 in exponential form is:

13954 = 2¹ × 6977¹

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 13954

List of positive integer factors of 13954 that divides 13940 without a remainder.

1, 2, 6977

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13940 and 13954. The biggest common factor number is the GCF number.
So the greatest common factor 13940 and 13954 is 2.

Also check out the Least Common Multiple of 13940 and 13954