What is the Greatest Common Factor of 13914 and 13923?

Greatest common factor (GCF) of 13914 and 13923 is 9.

GCF(13914,13923) = 9

We will now calculate the prime factors of 13914 and 13923, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13914 and 13923.

How to find the GCF of 13914 and 13923?

We will first find the prime factorization of 13914 and 13923. After we will calculate the factors of 13914 and 13923 and find the biggest common factor number .

Step-1: Prime Factorization of 13914

Prime factors of 13914 are 2, 3, 773. Prime factorization of 13914 in exponential form is:

13914 = 2¹ × 3² × 773¹

Step-2: Prime Factorization of 13923

Prime factors of 13923 are 3, 7, 13, 17. Prime factorization of 13923 in exponential form is:

13923 = 3² × 7¹ × 13¹ × 17¹

Step-3: Factors of 13914

List of positive integer factors of 13914 that divides 13914 without a remainder.

1, 2, 3, 6, 9, 18, 773, 1546, 2319, 4638, 6957

Step-4: Factors of 13923

List of positive integer factors of 13923 that divides 13914 without a remainder.

1, 3, 7, 9, 13, 17, 21, 39, 51, 63, 91, 117, 119, 153, 221, 273, 357, 663, 819, 1071, 1547, 1989, 4641

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13914 and 13923. The biggest common factor number is the GCF number.
So the greatest common factor 13914 and 13923 is 9.

Also check out the Least Common Multiple of 13914 and 13923