What is the Greatest Common Factor of 85189 and 85200?

Greatest common factor (GCF) of 85189 and 85200 is 1.

GCF(85189,85200) = 1

We will now calculate the prime factors of 85189 and 85200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85189 and 85200.

How to find the GCF of 85189 and 85200?

We will first find the prime factorization of 85189 and 85200. After we will calculate the factors of 85189 and 85200 and find the biggest common factor number .

Step-1: Prime Factorization of 85189

Prime factors of 85189 are 13, 6553. Prime factorization of 85189 in exponential form is:

85189 = 13¹ × 6553¹

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 85189

List of positive integer factors of 85189 that divides 85189 without a remainder.

1, 13, 6553

Step-4: Factors of 85200

List of positive integer factors of 85200 that divides 85189 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 85189 and 85200. The biggest common factor number is the GCF number.
So the greatest common factor 85189 and 85200 is 1.

Also check out the Least Common Multiple of 85189 and 85200