What is the Greatest Common Factor of 85200 and 85212?

Greatest common factor (GCF) of 85200 and 85212 is 12.

GCF(85200,85212) = 12

We will now calculate the prime factors of 85200 and 85212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85200 and 85212.

How to find the GCF of 85200 and 85212?

We will first find the prime factorization of 85200 and 85212. After we will calculate the factors of 85200 and 85212 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 85212

Prime factors of 85212 are 2, 3, 263. Prime factorization of 85212 in exponential form is:

85212 = 2² × 3⁴ × 263¹

Step-3: Factors of 85200

List of positive integer factors of 85200 that divides 85200 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

Step-4: Factors of 85212

List of positive integer factors of 85212 that divides 85200 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 263, 324, 526, 789, 1052, 1578, 2367, 3156, 4734, 7101, 9468, 14202, 21303, 28404, 42606

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85200 and 85212. The biggest common factor number is the GCF number.
So the greatest common factor 85200 and 85212 is 12.

Also check out the Least Common Multiple of 85200 and 85212