What is the Greatest Common Factor of 89184 and 89200?

Greatest common factor (GCF) of 89184 and 89200 is 16.

GCF(89184,89200) = 16

We will now calculate the prime factors of 89184 and 89200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89184 and 89200.

How to find the GCF of 89184 and 89200?

We will first find the prime factorization of 89184 and 89200. After we will calculate the factors of 89184 and 89200 and find the biggest common factor number .

Step-1: Prime Factorization of 89184

Prime factors of 89184 are 2, 3, 929. Prime factorization of 89184 in exponential form is:

89184 = 2⁵ × 3¹ × 929¹

Step-2: Prime Factorization of 89200

Prime factors of 89200 are 2, 5, 223. Prime factorization of 89200 in exponential form is:

89200 = 2⁴ × 5² × 223¹

Step-3: Factors of 89184

List of positive integer factors of 89184 that divides 89184 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 929, 1858, 2787, 3716, 5574, 7432, 11148, 14864, 22296, 29728, 44592

Step-4: Factors of 89200

List of positive integer factors of 89200 that divides 89184 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 223, 400, 446, 892, 1115, 1784, 2230, 3568, 4460, 5575, 8920, 11150, 17840, 22300, 44600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89184 and 89200. The biggest common factor number is the GCF number.
So the greatest common factor 89184 and 89200 is 16.

Also check out the Least Common Multiple of 89184 and 89200