What is the Greatest Common Factor of 17100 and 17114?

Greatest common factor (GCF) of 17100 and 17114 is 2.

GCF(17100,17114) = 2

We will now calculate the prime factors of 17100 and 17114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17100 and 17114.

How to find the GCF of 17100 and 17114?

We will first find the prime factorization of 17100 and 17114. After we will calculate the factors of 17100 and 17114 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 17114

Prime factors of 17114 are 2, 43, 199. Prime factorization of 17114 in exponential form is:

17114 = 2¹ × 43¹ × 199¹

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 17114

List of positive integer factors of 17114 that divides 17100 without a remainder.

1, 2, 43, 86, 199, 398, 8557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17100 and 17114. The biggest common factor number is the GCF number.
So the greatest common factor 17100 and 17114 is 2.

Also check out the Least Common Multiple of 17100 and 17114