What are the Factors of 2400?

The following are the different types of factors of 2400:

• Factors of 2400: 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, 2400

• Sum of Factors of 2400: 7812

• Negative Factors of 2400: -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, -2400

• Prime Factors of 2400: 2, 3, 5

• Prime Factorization of 2400: 2^5 × 3^1 × 5^2

There are two ways to find the factors of 2400: using factor pairs, and using prime factorization.

Factor pairs of 2400 are any two numbers that, when multiplied together, equal 2400. The question to ask is “what two numbers multiplied together equal 2400?” Every factor can be paired with another factor, and multiplying the two will result in 2400.

To find the factor pairs of 2400, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2400. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 2400 by the smallest prime factor, in this case, 2:

2400 ÷ 2 = 1200

2 and 1200 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 1200 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1200 by that number. In this case, 2 is the new smallest prime factor:

1200 ÷ 2 = 600

Remember that this new factor pair is only for the factors of 1200, not 2400. So, to finish the factor pair for 2400, you’d multiply 2 and 2 before pairing with 600:

2 x 2 = 4

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 2400:

(1, 2400), (2, 1200), (3, 800), (4, 600), (5, 480), (6, 400), (8, 300), (10, 240), (12, 200), (15, 160), (16, 150), (20, 120), (24, 100), (25, 96), (30, 80), (32, 75), (40, 60), (48, 50)

So, to list all the factors of 2400: 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, 2400

The negative factors of 2400 would be: -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, -2400

To find the Prime factorization of 2400, we break down all the factors of 2400 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.

The process of finding the prime factorization of 2400 only has a few differences from the above method of finding the factors of 2400. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 2400:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2400. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 2400 by the smallest prime factor, in this case, 2

2400 ÷ 2 = 1200

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 1200 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1200 by that number. The smallest prime factor you pick for 1200 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 2400 are: 2, 3, 5

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98

Factors of 68 - The factors of 68 are 1, 2, 4, 17, 34, 68

Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45