What is the Greatest Common Factor of 13909 and 13916?

Greatest common factor (GCF) of 13909 and 13916 is 7.

GCF(13909,13916) = 7

We will now calculate the prime factors of 13909 and 13916, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13909 and 13916.

How to find the GCF of 13909 and 13916?

We will first find the prime factorization of 13909 and 13916. After we will calculate the factors of 13909 and 13916 and find the biggest common factor number .

Step-1: Prime Factorization of 13909

Prime factors of 13909 are 7, 1987. Prime factorization of 13909 in exponential form is:

13909 = 7¹ × 1987¹

Step-2: Prime Factorization of 13916

Prime factors of 13916 are 2, 7, 71. Prime factorization of 13916 in exponential form is:

13916 = 2² × 7² × 71¹

Step-3: Factors of 13909

List of positive integer factors of 13909 that divides 13909 without a remainder.

1, 7, 1987

Step-4: Factors of 13916

List of positive integer factors of 13916 that divides 13909 without a remainder.

1, 2, 4, 7, 14, 28, 49, 71, 98, 142, 196, 284, 497, 994, 1988, 3479, 6958

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13909 and 13916. The biggest common factor number is the GCF number.
So the greatest common factor 13909 and 13916 is 7.

Also check out the Least Common Multiple of 13909 and 13916