What is the Greatest Common Factor of 66900 and 66912?

Greatest common factor (GCF) of 66900 and 66912 is 12.

GCF(66900,66912) = 12

We will now calculate the prime factors of 66900 and 66912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66900 and 66912.

How to find the GCF of 66900 and 66912?

We will first find the prime factorization of 66900 and 66912. After we will calculate the factors of 66900 and 66912 and find the biggest common factor number .

Step-1: Prime Factorization of 66900

Prime factors of 66900 are 2, 3, 5, 223. Prime factorization of 66900 in exponential form is:

66900 = 2² × 3¹ × 5² × 223¹

Step-2: Prime Factorization of 66912

Prime factors of 66912 are 2, 3, 17, 41. Prime factorization of 66912 in exponential form is:

66912 = 2⁵ × 3¹ × 17¹ × 41¹

Step-3: Factors of 66900

List of positive integer factors of 66900 that divides 66900 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 223, 300, 446, 669, 892, 1115, 1338, 2230, 2676, 3345, 4460, 5575, 6690, 11150, 13380, 16725, 22300, 33450

Step-4: Factors of 66912

List of positive integer factors of 66912 that divides 66900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 41, 48, 51, 68, 82, 96, 102, 123, 136, 164, 204, 246, 272, 328, 408, 492, 544, 656, 697, 816, 984, 1312, 1394, 1632, 1968, 2091, 2788, 3936, 4182, 5576, 8364, 11152, 16728, 22304, 33456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66900 and 66912. The biggest common factor number is the GCF number.
So the greatest common factor 66900 and 66912 is 12.

Also check out the Least Common Multiple of 66900 and 66912