What is the Greatest Common Factor of 2400 and 2415?

Greatest common factor (GCF) of 2400 and 2415 is 15.

GCF(2400,2415) = 15

We will now calculate the prime factors of 2400 and 2415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2400 and 2415.

How to find the GCF of 2400 and 2415?

We will first find the prime factorization of 2400 and 2415. After we will calculate the factors of 2400 and 2415 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 2415

Prime factors of 2415 are 3, 5, 7, 23. Prime factorization of 2415 in exponential form is:

2415 = 3¹ × 5¹ × 7¹ × 23¹

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 2415

List of positive integer factors of 2415 that divides 2400 without a remainder.

1, 3, 5, 7, 15, 21, 23, 35, 69, 105, 115, 161, 345, 483, 805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2400 and 2415. The biggest common factor number is the GCF number.
So the greatest common factor 2400 and 2415 is 15.

Also check out the Least Common Multiple of 2400 and 2415