What is the Greatest Common Factor of 83200 and 83220?

Greatest common factor (GCF) of 83200 and 83220 is 20.

GCF(83200,83220) = 20

We will now calculate the prime factors of 83200 and 83220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83200 and 83220.

How to find the GCF of 83200 and 83220?

We will first find the prime factorization of 83200 and 83220. After we will calculate the factors of 83200 and 83220 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 83220

Prime factors of 83220 are 2, 3, 5, 19, 73. Prime factorization of 83220 in exponential form is:

83220 = 2² × 3¹ × 5¹ × 19¹ × 73¹

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 83220

List of positive integer factors of 83220 that divides 83200 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 73, 76, 95, 114, 146, 190, 219, 228, 285, 292, 365, 380, 438, 570, 730, 876, 1095, 1140, 1387, 1460, 2190, 2774, 4161, 4380, 5548, 6935, 8322, 13870, 16644, 20805, 27740, 41610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83200 and 83220. The biggest common factor number is the GCF number.
So the greatest common factor 83200 and 83220 is 20.

Also check out the Least Common Multiple of 83200 and 83220