What is the Greatest Common Factor of 83200 and 83210?

Greatest common factor (GCF) of 83200 and 83210 is 10.

GCF(83200,83210) = 10

We will now calculate the prime factors of 83200 and 83210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83210.

How to find the GCF of 83200 and 83210?

We will first find the prime factorization of 83200 and 83210. After we will calculate the factors of 83200 and 83210 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 83210

Prime factors of 83210 are 2, 5, 53, 157. Prime factorization of 83210 in exponential form is:

83210 = 2¹ × 5¹ × 53¹ × 157¹

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 83210

List of positive integer factors of 83210 that divides 83200 without a remainder.

1, 2, 5, 10, 53, 106, 157, 265, 314, 530, 785, 1570, 8321, 16642, 41605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83210. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83210 is 10.

Also check out the Least Common Multiple of 83200 and 83210