What is the Greatest Common Factor of 83200 and 83204?

Greatest common factor (GCF) of 83200 and 83204 is 4.

GCF(83200,83204) = 4

We will now calculate the prime factors of 83200 and 83204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83204.

How to find the GCF of 83200 and 83204?

We will first find the prime factorization of 83200 and 83204. After we will calculate the factors of 83200 and 83204 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 83204

Prime factors of 83204 are 2, 11, 31, 61. Prime factorization of 83204 in exponential form is:

83204 = 2² × 11¹ × 31¹ × 61¹

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 83204

List of positive integer factors of 83204 that divides 83200 without a remainder.

1, 2, 4, 11, 22, 31, 44, 61, 62, 122, 124, 244, 341, 671, 682, 1342, 1364, 1891, 2684, 3782, 7564, 20801, 41602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83204. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83204 is 4.

Also check out the Least Common Multiple of 83200 and 83204