What is the Greatest Common Factor of 83200 and 83216?

Greatest common factor (GCF) of 83200 and 83216 is 16.

GCF(83200,83216) = 16

We will now calculate the prime factors of 83200 and 83216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83216.

How to find the GCF of 83200 and 83216?

We will first find the prime factorization of 83200 and 83216. After we will calculate the factors of 83200 and 83216 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 83216

Prime factors of 83216 are 2, 7, 743. Prime factorization of 83216 in exponential form is:

83216 = 2⁴ × 7¹ × 743¹

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 83216

List of positive integer factors of 83216 that divides 83200 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 743, 1486, 2972, 5201, 5944, 10402, 11888, 20804, 41608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83216. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83216 is 16.

Also check out the Least Common Multiple of 83200 and 83216