What is the Greatest Common Factor of 12090 and 12100?

Greatest common factor (GCF) of 12090 and 12100 is 10.

GCF(12090,12100) = 10

We will now calculate the prime factors of 12090 and 12100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12090 and 12100.

How to find the GCF of 12090 and 12100?

We will first find the prime factorization of 12090 and 12100. After we will calculate the factors of 12090 and 12100 and find the biggest common factor number .

Step-1: Prime Factorization of 12090

Prime factors of 12090 are 2, 3, 5, 13, 31. Prime factorization of 12090 in exponential form is:

12090 = 2¹ × 3¹ × 5¹ × 13¹ × 31¹

Step-2: Prime Factorization of 12100

Prime factors of 12100 are 2, 5, 11. Prime factorization of 12100 in exponential form is:

12100 = 2² × 5² × 11²

Step-3: Factors of 12090

List of positive integer factors of 12090 that divides 12090 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 31, 39, 62, 65, 78, 93, 130, 155, 186, 195, 310, 390, 403, 465, 806, 930, 1209, 2015, 2418, 4030, 6045

Step-4: Factors of 12100

List of positive integer factors of 12100 that divides 12090 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12090 and 12100. The biggest common factor number is the GCF number.
So the greatest common factor 12090 and 12100 is 10.

Also check out the Least Common Multiple of 12090 and 12100