What is the Greatest Common Factor of 19129 and 19138?

Greatest common factor (GCF) of 19129 and 19138 is 1.

GCF(19129,19138) = 1

We will now calculate the prime factors of 19129 and 19138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19129 and 19138.

How to find the GCF of 19129 and 19138?

We will first find the prime factorization of 19129 and 19138. After we will calculate the factors of 19129 and 19138 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 19138

Prime factors of 19138 are 2, 7, 1367. Prime factorization of 19138 in exponential form is:

19138 = 2¹ × 7¹ × 1367¹

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 19138

List of positive integer factors of 19138 that divides 19129 without a remainder.

1, 2, 7, 14, 1367, 2734, 9569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19129 and 19138. The biggest common factor number is the GCF number.
So the greatest common factor 19129 and 19138 is 1.

Also check out the Least Common Multiple of 19129 and 19138