What is the Greatest Common Factor of 12400 and 12420?

Greatest common factor (GCF) of 12400 and 12420 is 20.

GCF(12400,12420) = 20

We will now calculate the prime factors of 12400 and 12420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12400 and 12420.

How to find the GCF of 12400 and 12420?

We will first find the prime factorization of 12400 and 12420. After we will calculate the factors of 12400 and 12420 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12420

Prime factors of 12420 are 2, 3, 5, 23. Prime factorization of 12420 in exponential form is:

12420 = 2² × 3³ × 5¹ × 23¹

Step-3: Factors of 12400

List of positive integer factors of 12400 that divides 12400 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

Step-4: Factors of 12420

List of positive integer factors of 12420 that divides 12400 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 27, 30, 36, 45, 46, 54, 60, 69, 90, 92, 108, 115, 135, 138, 180, 207, 230, 270, 276, 345, 414, 460, 540, 621, 690, 828, 1035, 1242, 1380, 2070, 2484, 3105, 4140, 6210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12400 and 12420. The biggest common factor number is the GCF number.
So the greatest common factor 12400 and 12420 is 20.

Also check out the Least Common Multiple of 12400 and 12420