What is the Greatest Common Factor of 12400 and 12405?

Greatest common factor (GCF) of 12400 and 12405 is 5.

GCF(12400,12405) = 5

We will now calculate the prime factors of 12400 and 12405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12400 and 12405.

How to find the GCF of 12400 and 12405?

We will first find the prime factorization of 12400 and 12405. After we will calculate the factors of 12400 and 12405 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 12405

Prime factors of 12405 are 3, 5, 827. Prime factorization of 12405 in exponential form is:

12405 = 3¹ × 5¹ × 827¹

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 12405

List of positive integer factors of 12405 that divides 12400 without a remainder.

1, 3, 5, 15, 827, 2481, 4135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12400 and 12405. The biggest common factor number is the GCF number.
So the greatest common factor 12400 and 12405 is 5.

Also check out the Least Common Multiple of 12400 and 12405