What is the Greatest Common Factor of 17119 and 17138?

Greatest common factor (GCF) of 17119 and 17138 is 19.

GCF(17119,17138) = 19

We will now calculate the prime factors of 17119 and 17138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17119 and 17138.

How to find the GCF of 17119 and 17138?

We will first find the prime factorization of 17119 and 17138. After we will calculate the factors of 17119 and 17138 and find the biggest common factor number .

Step-1: Prime Factorization of 17119

Prime factors of 17119 are 17, 19, 53. Prime factorization of 17119 in exponential form is:

17119 = 17¹ × 19¹ × 53¹

Step-2: Prime Factorization of 17138

Prime factors of 17138 are 2, 11, 19, 41. Prime factorization of 17138 in exponential form is:

17138 = 2¹ × 11¹ × 19¹ × 41¹

Step-3: Factors of 17119

List of positive integer factors of 17119 that divides 17119 without a remainder.

1, 17, 19, 53, 323, 901, 1007

Step-4: Factors of 17138

List of positive integer factors of 17138 that divides 17119 without a remainder.

1, 2, 11, 19, 22, 38, 41, 82, 209, 418, 451, 779, 902, 1558, 8569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17119 and 17138. The biggest common factor number is the GCF number.
So the greatest common factor 17119 and 17138 is 19.

Also check out the Least Common Multiple of 17119 and 17138