What is the Greatest Common Factor of 83200 and 83205?

Greatest common factor (GCF) of 83200 and 83205 is 5.

GCF(83200,83205) = 5

We will now calculate the prime factors of 83200 and 83205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83205.

How to find the GCF of 83200 and 83205?

We will first find the prime factorization of 83200 and 83205. After we will calculate the factors of 83200 and 83205 and find the biggest common factor number .

Step-1: Prime Factorization of 83200

Prime factors of 83200 are 2, 5, 13. Prime factorization of 83200 in exponential form is:

83200 = 2⁸ × 5² × 13¹

Step-2: Prime Factorization of 83205

Prime factors of 83205 are 3, 5, 43. Prime factorization of 83205 in exponential form is:

83205 = 3² × 5¹ × 43²

Step-3: Factors of 83200

List of positive integer factors of 83200 that divides 83200 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 128, 130, 160, 200, 208, 256, 260, 320, 325, 400, 416, 520, 640, 650, 800, 832, 1040, 1280, 1300, 1600, 1664, 2080, 2600, 3200, 3328, 4160, 5200, 6400, 8320, 10400, 16640, 20800, 41600

Step-4: Factors of 83205

List of positive integer factors of 83205 that divides 83200 without a remainder.

1, 3, 5, 9, 15, 43, 45, 129, 215, 387, 645, 1849, 1935, 5547, 9245, 16641, 27735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83205. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83205 is 5.

Also check out the Least Common Multiple of 83200 and 83205