Factors of 2400 are 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, and 2400

How to find factors of a number

1. Steps to find factors of 2400 using Division Method

Example: Find factors of 2400

  • Divide 2400 by 1: 2400 ÷ 1 : Remainder = 0
  • Divide 2400 by 2: 2400 ÷ 2 : Remainder = 0
  • Divide 2400 by 3: 2400 ÷ 3 : Remainder = 0
  • Divide 2400 by 4: 2400 ÷ 4 : Remainder = 0
  • Divide 2400 by 5: 2400 ÷ 5 : Remainder = 0
  • Divide 2400 by 6: 2400 ÷ 6 : Remainder = 0
  • Divide 2400 by 8: 2400 ÷ 8 : Remainder = 0
  • Divide 2400 by 10: 2400 ÷ 10 : Remainder = 0
  • Divide 2400 by 12: 2400 ÷ 12 : Remainder = 0
  • Divide 2400 by 15: 2400 ÷ 15 : Remainder = 0
  • Divide 2400 by 16: 2400 ÷ 16 : Remainder = 0
  • Divide 2400 by 20: 2400 ÷ 20 : Remainder = 0
  • Divide 2400 by 24: 2400 ÷ 24 : Remainder = 0
  • Divide 2400 by 25: 2400 ÷ 25 : Remainder = 0
  • Divide 2400 by 30: 2400 ÷ 30 : Remainder = 0
  • Divide 2400 by 32: 2400 ÷ 32 : Remainder = 0
  • Divide 2400 by 40: 2400 ÷ 40 : Remainder = 0
  • Divide 2400 by 48: 2400 ÷ 48 : Remainder = 0
  • Divide 2400 by 50: 2400 ÷ 50 : Remainder = 0
  • Divide 2400 by 60: 2400 ÷ 60 : Remainder = 0
  • Divide 2400 by 75: 2400 ÷ 75 : Remainder = 0
  • Divide 2400 by 80: 2400 ÷ 80 : Remainder = 0
  • Divide 2400 by 96: 2400 ÷ 96 : Remainder = 0
  • Divide 2400 by 100: 2400 ÷ 100 : Remainder = 0
  • Divide 2400 by 120: 2400 ÷ 120 : Remainder = 0
  • Divide 2400 by 150: 2400 ÷ 150 : Remainder = 0
  • Divide 2400 by 160: 2400 ÷ 160 : Remainder = 0
  • Divide 2400 by 200: 2400 ÷ 200 : Remainder = 0
  • Divide 2400 by 240: 2400 ÷ 240 : Remainder = 0
  • Divide 2400 by 300: 2400 ÷ 300 : Remainder = 0
  • Divide 2400 by 400: 2400 ÷ 400 : Remainder = 0
  • Divide 2400 by 480: 2400 ÷ 480 : Remainder = 0
  • Divide 2400 by 600: 2400 ÷ 600 : Remainder = 0
  • Divide 2400 by 800: 2400 ÷ 800 : Remainder = 0
  • Divide 2400 by 1200: 2400 ÷ 1200 : Remainder = 0
  • Divide 2400 by 2400: 2400 ÷ 2400 : Remainder = 0

Hence, Factors of 2400 are 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, and 2400

2. Steps to find factors of 2400 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 2400 using the division method, follow these steps:

  • Step 1. Start dividing 2400 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 2400, which is 2. Divide 2400 by 2 to obtain the quotient (1200).
    2400 ÷ 2 = 1200
  • Step 3. Repeat step 1 with the obtained quotient (1200).
    1200 ÷ 2 = 600
    600 ÷ 2 = 300
    300 ÷ 2 = 150
    150 ÷ 2 = 75
    75 ÷ 3 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 2400 is, 2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2400 as shown below:

So, the prime factorization of 2400 is, 2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5.

3. Find factors of 2400 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 2400 would be the two numbers which, when multiplied, give 2400 as the result.

The following table represents the calculation of factors of 2400 in pairs:

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

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 2400. They are called negative pair factors.

Hence, the negative pairs of 2400 would be ( -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 ) and ( -48 , -50 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 2400 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2400.
  • Every number is a factor of zero (0), since 2400 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 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 are exact divisors of 2400.
  • Factors of 2400 are 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. Each factor divides 2400 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 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 are all less than or equal to 2400.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -2400 )?

    Factors of -2400 are -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.

  • What is the sum of all factors of 2400?

    The sum of all factors of 2400 is 7812.

  • What is prime factorization of 2400?

    Prime factorization of 2400 is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5.

  • What are the pair factors of 2400?

    Pair factors of 2400 are (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).

  • What are six multiples of 2400?

    First five multiples of 2400 are 4800, 7200, 9600, 12000, 14400, 16800.

  • Is 2400 a whole number?

    Yes 2400 is a whole number.

  • Which is the smallest prime factor of 2400?

    Smallest prime factor of 2400 is 2.

  • What are five multiples of 2400?

    First five multiples of 2400 are 4800, 7200, 9600, 12000, 14400.

  • Write all factors of 2400?

    Factors of 2400 are 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.

Examples of Factors

Joey wants to write all the prime factors of 2400 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2400 are 2, 2, 2, 2, 2, 3, 5, 5.
So in exponential form it can be written as 25 x 3 x 52.

How many factors are there for 2400?

Factors of 2400 are 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.
So there are in total 36 factors.

Kevin has been asked to write 35 factor(s) of 2400. Can you predict the answer?

35 factor(s) of 2400 are 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.

Sammy is puzzled while calculating the prime factors of 2400. Can you help him find them?

Factors of 2400 are 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 are 2, 2, 2, 2, 2, 3, 5, 5

What is prime factorization of 2400?

Prime factorization of 2400 is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 = 25 x 3 x 52.

Ariel has been assigned the task to find the product of all the prime factors of 2400. Can you help her?

Prime factors of 2400 are 2, 2, 2, 2, 2, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 2400?

Factors of 2400 are 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.
Even factors of 2400 are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 50, 60, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400.
Hence, product of even factors of 2400 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 20 x 24 x 30 x 32 x 40 x 48 x 50 x 60 x 80 x 96 x 100 x 120 x 150 x 160 x 200 x 240 x 300 x 400 x 480 x 600 x 800 x 1200 x 2400 = 1.6543163447903718e+55.