What is the Greatest Common Factor of 12390 and 12400?

Greatest common factor (GCF) of 12390 and 12400 is 10.

GCF(12390,12400) = 10

We will now calculate the prime factors of 12390 and 12400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12390 and 12400.

How to find the GCF of 12390 and 12400?

We will first find the prime factorization of 12390 and 12400. After we will calculate the factors of 12390 and 12400 and find the biggest common factor number .

Step-1: Prime Factorization of 12390

Prime factors of 12390 are 2, 3, 5, 7, 59. Prime factorization of 12390 in exponential form is:

12390 = 2¹ × 3¹ × 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 12400

Prime factors of 12400 are 2, 5, 31. Prime factorization of 12400 in exponential form is:

12400 = 2⁴ × 5² × 31¹

Step-3: Factors of 12390

List of positive integer factors of 12390 that divides 12390 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 59, 70, 105, 118, 177, 210, 295, 354, 413, 590, 826, 885, 1239, 1770, 2065, 2478, 4130, 6195

Step-4: Factors of 12400

List of positive integer factors of 12400 that divides 12390 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 31, 40, 50, 62, 80, 100, 124, 155, 200, 248, 310, 400, 496, 620, 775, 1240, 1550, 2480, 3100, 6200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12390 and 12400. The biggest common factor number is the GCF number.
So the greatest common factor 12390 and 12400 is 10.

Also check out the Least Common Multiple of 12390 and 12400