What is the Greatest Common Factor of 8190 and 8200?

Greatest common factor (GCF) of 8190 and 8200 is 10.

GCF(8190,8200) = 10

We will now calculate the prime factors of 8190 and 8200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8190 and 8200.

How to find the GCF of 8190 and 8200?

We will first find the prime factorization of 8190 and 8200. After we will calculate the factors of 8190 and 8200 and find the biggest common factor number .

Step-1: Prime Factorization of 8190

Prime factors of 8190 are 2, 3, 5, 7, 13. Prime factorization of 8190 in exponential form is:

8190 = 2¹ × 3² × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 8200

Prime factors of 8200 are 2, 5, 41. Prime factorization of 8200 in exponential form is:

8200 = 2³ × 5² × 41¹

Step-3: Factors of 8190

List of positive integer factors of 8190 that divides 8190 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 13, 14, 15, 18, 21, 26, 30, 35, 39, 42, 45, 63, 65, 70, 78, 90, 91, 105, 117, 126, 130, 182, 195, 210, 234, 273, 315, 390, 455, 546, 585, 630, 819, 910, 1170, 1365, 1638, 2730, 4095

Step-4: Factors of 8200

List of positive integer factors of 8200 that divides 8190 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 41, 50, 82, 100, 164, 200, 205, 328, 410, 820, 1025, 1640, 2050, 4100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8190 and 8200. The biggest common factor number is the GCF number.
So the greatest common factor 8190 and 8200 is 10.

Also check out the Least Common Multiple of 8190 and 8200