What is the Greatest Common Factor of 19409 and 19422?

Greatest common factor (GCF) of 19409 and 19422 is 13.

GCF(19409,19422) = 13

We will now calculate the prime factors of 19409 and 19422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19409 and 19422.

How to find the GCF of 19409 and 19422?

We will first find the prime factorization of 19409 and 19422. After we will calculate the factors of 19409 and 19422 and find the biggest common factor number .

Step-1: Prime Factorization of 19409

Prime factors of 19409 are 13, 1493. Prime factorization of 19409 in exponential form is:

19409 = 13¹ × 1493¹

Step-2: Prime Factorization of 19422

Prime factors of 19422 are 2, 3, 13, 83. Prime factorization of 19422 in exponential form is:

19422 = 2¹ × 3² × 13¹ × 83¹

Step-3: Factors of 19409

List of positive integer factors of 19409 that divides 19409 without a remainder.

1, 13, 1493

Step-4: Factors of 19422

List of positive integer factors of 19422 that divides 19409 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 83, 117, 166, 234, 249, 498, 747, 1079, 1494, 2158, 3237, 6474, 9711

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19409 and 19422. The biggest common factor number is the GCF number.
So the greatest common factor 19409 and 19422 is 13.

Also check out the Least Common Multiple of 19409 and 19422