What is the Greatest Common Factor of 2400 and 2405?

Greatest common factor (GCF) of 2400 and 2405 is 5.

GCF(2400,2405) = 5

We will now calculate the prime factors of 2400 and 2405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2400 and 2405.

How to find the GCF of 2400 and 2405?

We will first find the prime factorization of 2400 and 2405. After we will calculate the factors of 2400 and 2405 and find the biggest common factor number .

Step-1: Prime Factorization of 2400

Prime factors of 2400 are 2, 3, 5. Prime factorization of 2400 in exponential form is:

2400 = 2⁵ × 3¹ × 5²

Step-2: Prime Factorization of 2405

Prime factors of 2405 are 5, 13, 37. Prime factorization of 2405 in exponential form is:

2405 = 5¹ × 13¹ × 37¹

Step-3: Factors of 2400

List of positive integer factors of 2400 that divides 2400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200

Step-4: Factors of 2405

List of positive integer factors of 2405 that divides 2400 without a remainder.

1, 5, 13, 37, 65, 185, 481

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2400 and 2405. The biggest common factor number is the GCF number.
So the greatest common factor 2400 and 2405 is 5.

Also check out the Least Common Multiple of 2400 and 2405