What is the Greatest Common Factor of 17100 and 17119?

Greatest common factor (GCF) of 17100 and 17119 is 19.

GCF(17100,17119) = 19

We will now calculate the prime factors of 17100 and 17119, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17100 and 17119.

How to find the GCF of 17100 and 17119?

We will first find the prime factorization of 17100 and 17119. After we will calculate the factors of 17100 and 17119 and find the biggest common factor number .

Step-1: Prime Factorization of 17100

Prime factors of 17100 are 2, 3, 5, 19. Prime factorization of 17100 in exponential form is:

17100 = 2² × 3² × 5² × 19¹

Step-2: 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-3: Factors of 17100

List of positive integer factors of 17100 that divides 17100 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, 8550

Step-4: Factors of 17119

List of positive integer factors of 17119 that divides 17100 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17100 and 17119. The biggest common factor number is the GCF number.
So the greatest common factor 17100 and 17119 is 19.

Also check out the Least Common Multiple of 17100 and 17119