What is the Greatest Common Factor of 85200 and 85209?

Greatest common factor (GCF) of 85200 and 85209 is 3.

GCF(85200,85209) = 3

We will now calculate the prime factors of 85200 and 85209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85200 and 85209.

How to find the GCF of 85200 and 85209?

We will first find the prime factorization of 85200 and 85209. After we will calculate the factors of 85200 and 85209 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 85209

Prime factors of 85209 are 3, 28403. Prime factorization of 85209 in exponential form is:

85209 = 3¹ × 28403¹

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 85209

List of positive integer factors of 85209 that divides 85200 without a remainder.

1, 3, 28403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85200 and 85209. The biggest common factor number is the GCF number.
So the greatest common factor 85200 and 85209 is 3.

Also check out the Least Common Multiple of 85200 and 85209