What is the Greatest Common Factor of 2385 and 2400?

Greatest common factor (GCF) of 2385 and 2400 is 15.

GCF(2385,2400) = 15

We will now calculate the prime factors of 2385 and 2400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2385 and 2400.

How to find the GCF of 2385 and 2400?

We will first find the prime factorization of 2385 and 2400. After we will calculate the factors of 2385 and 2400 and find the biggest common factor number .

Step-1: Prime Factorization of 2385

Prime factors of 2385 are 3, 5, 53. Prime factorization of 2385 in exponential form is:

2385 = 3² × 5¹ × 53¹

Step-2: 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-3: Factors of 2385

List of positive integer factors of 2385 that divides 2385 without a remainder.

1, 3, 5, 9, 15, 45, 53, 159, 265, 477, 795

Step-4: Factors of 2400

List of positive integer factors of 2400 that divides 2385 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2385 and 2400. The biggest common factor number is the GCF number.
So the greatest common factor 2385 and 2400 is 15.

Also check out the Least Common Multiple of 2385 and 2400