What is the Greatest Common Factor of 13906 and 13923?

Greatest common factor (GCF) of 13906 and 13923 is 17.

GCF(13906,13923) = 17

We will now calculate the prime factors of 13906 and 13923, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13906 and 13923.

How to find the GCF of 13906 and 13923?

We will first find the prime factorization of 13906 and 13923. After we will calculate the factors of 13906 and 13923 and find the biggest common factor number .

Step-1: Prime Factorization of 13906

Prime factors of 13906 are 2, 17, 409. Prime factorization of 13906 in exponential form is:

13906 = 2¹ × 17¹ × 409¹

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 13906

List of positive integer factors of 13906 that divides 13906 without a remainder.

1, 2, 17, 34, 409, 818, 6953

Step-4: Factors of 13923

List of positive integer factors of 13923 that divides 13906 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 13906 and 13923. The biggest common factor number is the GCF number.
So the greatest common factor 13906 and 13923 is 17.

Also check out the Least Common Multiple of 13906 and 13923