What is the Greatest Common Factor of 2400 and 2414?

Greatest common factor (GCF) of 2400 and 2414 is 2.

GCF(2400,2414) = 2

We will now calculate the prime factors of 2400 and 2414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2400 and 2414.

How to find the GCF of 2400 and 2414?

We will first find the prime factorization of 2400 and 2414. After we will calculate the factors of 2400 and 2414 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 2414

Prime factors of 2414 are 2, 17, 71. Prime factorization of 2414 in exponential form is:

2414 = 2¹ × 17¹ × 71¹

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 2414

List of positive integer factors of 2414 that divides 2400 without a remainder.

1, 2, 17, 34, 71, 142, 1207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2400 and 2414. The biggest common factor number is the GCF number.
So the greatest common factor 2400 and 2414 is 2.

Also check out the Least Common Multiple of 2400 and 2414