What is the Greatest Common Factor of 85200 and 85219?

Greatest common factor (GCF) of 85200 and 85219 is 1.

GCF(85200,85219) = 1

We will now calculate the prime factors of 85200 and 85219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85200 and 85219.

How to find the GCF of 85200 and 85219?

We will first find the prime factorization of 85200 and 85219. After we will calculate the factors of 85200 and 85219 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 85219

Prime factors of 85219 are 31, 2749. Prime factorization of 85219 in exponential form is:

85219 = 31¹ × 2749¹

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 85219

List of positive integer factors of 85219 that divides 85200 without a remainder.

1, 31, 2749

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85200 and 85219. The biggest common factor number is the GCF number.
So the greatest common factor 85200 and 85219 is 1.

Also check out the Least Common Multiple of 85200 and 85219