What is the Greatest Common Factor of 19136 and 19149?

Greatest common factor (GCF) of 19136 and 19149 is 13.

GCF(19136,19149) = 13

We will now calculate the prime factors of 19136 and 19149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19136 and 19149.

How to find the GCF of 19136 and 19149?

We will first find the prime factorization of 19136 and 19149. After we will calculate the factors of 19136 and 19149 and find the biggest common factor number .

Step-1: Prime Factorization of 19136

Prime factors of 19136 are 2, 13, 23. Prime factorization of 19136 in exponential form is:

19136 = 2⁶ × 13¹ × 23¹

Step-2: Prime Factorization of 19149

Prime factors of 19149 are 3, 13, 491. Prime factorization of 19149 in exponential form is:

19149 = 3¹ × 13¹ × 491¹

Step-3: Factors of 19136

List of positive integer factors of 19136 that divides 19136 without a remainder.

1, 2, 4, 8, 13, 16, 23, 26, 32, 46, 52, 64, 92, 104, 184, 208, 299, 368, 416, 598, 736, 832, 1196, 1472, 2392, 4784, 9568

Step-4: Factors of 19149

List of positive integer factors of 19149 that divides 19136 without a remainder.

1, 3, 13, 39, 491, 1473, 6383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19136 and 19149. The biggest common factor number is the GCF number.
So the greatest common factor 19136 and 19149 is 13.

Also check out the Least Common Multiple of 19136 and 19149