What is the Greatest Common Factor of 19129 and 19136?

Greatest common factor (GCF) of 19129 and 19136 is 1.

GCF(19129,19136) = 1

We will now calculate the prime factors of 19129 and 19136, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19129 and 19136.

How to find the GCF of 19129 and 19136?

We will first find the prime factorization of 19129 and 19136. After we will calculate the factors of 19129 and 19136 and find the biggest common factor number .

Step-1: Prime Factorization of 19129

Prime factors of 19129 are 11, 37, 47. Prime factorization of 19129 in exponential form is:

19129 = 11¹ × 37¹ × 47¹

Step-2: 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-3: Factors of 19129

List of positive integer factors of 19129 that divides 19129 without a remainder.

1, 11, 37, 47, 407, 517, 1739

Step-4: Factors of 19136

List of positive integer factors of 19136 that divides 19129 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19129 and 19136. The biggest common factor number is the GCF number.
So the greatest common factor 19129 and 19136 is 1.

Also check out the Least Common Multiple of 19129 and 19136