What is the Greatest Common Factor of 83190 and 83200?

Greatest common factor (GCF) of 83190 and 83200 is 10.

GCF(83190,83200) = 10

We will now calculate the prime factors of 83190 and 83200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83190 and 83200.

How to find the GCF of 83190 and 83200?

We will first find the prime factorization of 83190 and 83200. After we will calculate the factors of 83190 and 83200 and find the biggest common factor number .

Step-1: Prime Factorization of 83190

Prime factors of 83190 are 2, 3, 5, 47, 59. Prime factorization of 83190 in exponential form is:

83190 = 2¹ × 3¹ × 5¹ × 47¹ × 59¹

Step-2: 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-3: Factors of 83190

List of positive integer factors of 83190 that divides 83190 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 59, 94, 118, 141, 177, 235, 282, 295, 354, 470, 590, 705, 885, 1410, 1770, 2773, 5546, 8319, 13865, 16638, 27730, 41595

Step-4: Factors of 83200

List of positive integer factors of 83200 that divides 83190 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83190 and 83200. The biggest common factor number is the GCF number.
So the greatest common factor 83190 and 83200 is 10.

Also check out the Least Common Multiple of 83190 and 83200