What is the Greatest Common Factor of 17119 and 17136?

Greatest common factor (GCF) of 17119 and 17136 is 17.

GCF(17119,17136) = 17

We will now calculate the prime factors of 17119 and 17136, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17119 and 17136.

How to find the GCF of 17119 and 17136?

We will first find the prime factorization of 17119 and 17136. After we will calculate the factors of 17119 and 17136 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 17136

Prime factors of 17136 are 2, 3, 7, 17. Prime factorization of 17136 in exponential form is:

17136 = 2⁴ × 3² × 7¹ × 17¹

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 17136

List of positive integer factors of 17136 that divides 17119 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 17, 18, 21, 24, 28, 34, 36, 42, 48, 51, 56, 63, 68, 72, 84, 102, 112, 119, 126, 136, 144, 153, 168, 204, 238, 252, 272, 306, 336, 357, 408, 476, 504, 612, 714, 816, 952, 1008, 1071, 1224, 1428, 1904, 2142, 2448, 2856, 4284, 5712, 8568

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17119 and 17136. The biggest common factor number is the GCF number.
So the greatest common factor 17119 and 17136 is 17.

Also check out the Least Common Multiple of 17119 and 17136