What is the Greatest Common Factor of 17100 and 17112?

Greatest common factor (GCF) of 17100 and 17112 is 12.

GCF(17100,17112) = 12

We will now calculate the prime factors of 17100 and 17112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17100 and 17112.

How to find the GCF of 17100 and 17112?

We will first find the prime factorization of 17100 and 17112. After we will calculate the factors of 17100 and 17112 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 17112

Prime factors of 17112 are 2, 3, 23, 31. Prime factorization of 17112 in exponential form is:

17112 = 2³ × 3¹ × 23¹ × 31¹

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 17112

List of positive integer factors of 17112 that divides 17100 without a remainder.

1, 2, 3, 4, 6, 8, 12, 23, 24, 31, 46, 62, 69, 92, 93, 124, 138, 184, 186, 248, 276, 372, 552, 713, 744, 1426, 2139, 2852, 4278, 5704, 8556

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17100 and 17112. The biggest common factor number is the GCF number.
So the greatest common factor 17100 and 17112 is 12.

Also check out the Least Common Multiple of 17100 and 17112