What is the Greatest Common Factor of 12290 and 12300?

Greatest common factor (GCF) of 12290 and 12300 is 10.

GCF(12290,12300) = 10

We will now calculate the prime factors of 12290 and 12300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12290 and 12300.

How to find the GCF of 12290 and 12300?

We will first find the prime factorization of 12290 and 12300. After we will calculate the factors of 12290 and 12300 and find the biggest common factor number .

Step-1: Prime Factorization of 12290

Prime factors of 12290 are 2, 5, 1229. Prime factorization of 12290 in exponential form is:

12290 = 2¹ × 5¹ × 1229¹

Step-2: Prime Factorization of 12300

Prime factors of 12300 are 2, 3, 5, 41. Prime factorization of 12300 in exponential form is:

12300 = 2² × 3¹ × 5² × 41¹

Step-3: Factors of 12290

List of positive integer factors of 12290 that divides 12290 without a remainder.

1, 2, 5, 10, 1229, 2458, 6145

Step-4: Factors of 12300

List of positive integer factors of 12300 that divides 12290 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12290 and 12300. The biggest common factor number is the GCF number.
So the greatest common factor 12290 and 12300 is 10.

Also check out the Least Common Multiple of 12290 and 12300