What is the Greatest Common Factor of 85188 and 85200?

Greatest common factor (GCF) of 85188 and 85200 is 12.

GCF(85188,85200) = 12

We will now calculate the prime factors of 85188 and 85200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85188 and 85200.

How to find the GCF of 85188 and 85200?

We will first find the prime factorization of 85188 and 85200. After we will calculate the factors of 85188 and 85200 and find the biggest common factor number .

Step-1: Prime Factorization of 85188

Prime factors of 85188 are 2, 3, 31, 229. Prime factorization of 85188 in exponential form is:

85188 = 2² × 3¹ × 31¹ × 229¹

Step-2: Prime Factorization of 85200

Prime factors of 85200 are 2, 3, 5, 71. Prime factorization of 85200 in exponential form is:

85200 = 2⁴ × 3¹ × 5² × 71¹

Step-3: Factors of 85188

List of positive integer factors of 85188 that divides 85188 without a remainder.

1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 229, 372, 458, 687, 916, 1374, 2748, 7099, 14198, 21297, 28396, 42594

Step-4: Factors of 85200

List of positive integer factors of 85200 that divides 85188 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 71, 75, 80, 100, 120, 142, 150, 200, 213, 240, 284, 300, 355, 400, 426, 568, 600, 710, 852, 1065, 1136, 1200, 1420, 1704, 1775, 2130, 2840, 3408, 3550, 4260, 5325, 5680, 7100, 8520, 10650, 14200, 17040, 21300, 28400, 42600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85188 and 85200. The biggest common factor number is the GCF number.
So the greatest common factor 85188 and 85200 is 12.

Also check out the Least Common Multiple of 85188 and 85200