What is the Greatest Common Factor of 17700 and 17712?

Greatest common factor (GCF) of 17700 and 17712 is 12.

GCF(17700,17712) = 12

We will now calculate the prime factors of 17700 and 17712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17700 and 17712.

How to find the GCF of 17700 and 17712?

We will first find the prime factorization of 17700 and 17712. After we will calculate the factors of 17700 and 17712 and find the biggest common factor number .

Step-1: Prime Factorization of 17700

Prime factors of 17700 are 2, 3, 5, 59. Prime factorization of 17700 in exponential form is:

17700 = 2² × 3¹ × 5² × 59¹

Step-2: Prime Factorization of 17712

Prime factors of 17712 are 2, 3, 41. Prime factorization of 17712 in exponential form is:

17712 = 2⁴ × 3³ × 41¹

Step-3: Factors of 17700

List of positive integer factors of 17700 that divides 17700 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 59, 60, 75, 100, 118, 150, 177, 236, 295, 300, 354, 590, 708, 885, 1180, 1475, 1770, 2950, 3540, 4425, 5900, 8850

Step-4: Factors of 17712

List of positive integer factors of 17712 that divides 17700 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 41, 48, 54, 72, 82, 108, 123, 144, 164, 216, 246, 328, 369, 432, 492, 656, 738, 984, 1107, 1476, 1968, 2214, 2952, 4428, 5904, 8856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17700 and 17712. The biggest common factor number is the GCF number.
So the greatest common factor 17700 and 17712 is 12.

Also check out the Least Common Multiple of 17700 and 17712