What is the Greatest Common Factor of 85184 and 85200?

Greatest common factor (GCF) of 85184 and 85200 is 16.

GCF(85184,85200) = 16

We will now calculate the prime factors of 85184 and 85200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85184 and 85200.

How to find the GCF of 85184 and 85200?

We will first find the prime factorization of 85184 and 85200. After we will calculate the factors of 85184 and 85200 and find the biggest common factor number .

Step-1: Prime Factorization of 85184

Prime factors of 85184 are 2, 11. Prime factorization of 85184 in exponential form is:

85184 = 2⁶ × 11³

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 85184

List of positive integer factors of 85184 that divides 85184 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1331, 1936, 2662, 3872, 5324, 7744, 10648, 21296, 42592

Step-4: Factors of 85200

List of positive integer factors of 85200 that divides 85184 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 85184 and 85200. The biggest common factor number is the GCF number.
So the greatest common factor 85184 and 85200 is 16.

Also check out the Least Common Multiple of 85184 and 85200