Factors of 2400

The numbers that divide 2400 evenly are known as factors of 2400.

A factor of 2400 is a number that divides the number without remainder.

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

Negative factors of 2400: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -96, -100, -120, -150, -160, -200, -240, -300, -400, -480, -600, -800, -1200, and -2400.

Prime factors of 2400: 2, 3, and 5.

Prime factorization of 2400: 2^5 × 3 × 5^2.

The sum of factors of 2400: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 40 + 48 + 50 + 60 + 75 + 80 + 96 + 100 + 120 + 150 + 160 + 200 + 240 + 300 + 400 + 480 + 600 + 800 + 1200 + 2400 = 7440

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
   
• Finding factors using division method
   
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 2400. Identifying the numbers which are multiplied to get the number 2400 is the multiplication method.

Step 1: Multiply 2400 by 1, 2400 × 1 = 2400.

Step 2: Check for other numbers that give 2400 after multiplying         

2 × 1200 = 2400         

3 × 800 = 2400         

4 × 600 = 2400         

5 × 480 = 2400         

6 × 400 = 2400         

8 × 300 = 2400         

10 × 240 = 2400         

12 × 200 = 2400         

15 × 160 = 2400         

16 × 150 = 2400         

20 × 120 = 2400         

24 × 100 = 2400         

25 × 96 = 2400         

30 × 80 = 2400         

40 × 60 = 2400

Therefore, the positive factor pairs 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), and (40, 60).

For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method 

Step 1: Divide 2400 by 1, 2400 ÷ 1 = 2400.

Step 2: Continue dividing 2400 by the numbers until the remainder becomes 0.

2400 ÷ 1 = 2400

2400 ÷ 2 = 1200

2400 ÷ 3 = 800

2400 ÷ 4 = 600

2400 ÷ 5 = 480

2400 ÷ 6 = 400

2400 ÷ 8 = 300

2400 ÷ 10 = 240

2400 ÷ 12 = 200

2400 ÷ 15 = 160

2400 ÷ 16 = 150

2400 ÷ 20 = 120

2400 ÷ 24 = 100

2400 ÷ 25 = 96

2400 ÷ 30 = 80

2400 ÷ 40 = 60

Therefore, the factors of 2400 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, and 2400.

The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:

• Using prime factorization
   
• Using factor tree

Using Prime Factorization: In this process, prime factors of 2400 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

2400 ÷ 2 = 1200

1200 ÷ 2 = 600

600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

The prime factors of 2400 are 2, 3, and 5.

The prime factorization of 2400 is: 2^5 × 3 × 5^2.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows 

Step 1: Firstly, 2400 is divided by 2 to get 1200.

Step 2: Now divide 1200 by 2 to get 600.

Step 3: Then divide 600 by 2 to get 300.

Step 4: Divide 300 by 2 to get 150.

Step 5: Divide 150 by 2 to get 75.

Step 6: Divide 75 by 3 to get 25.

Step 7: Finally, divide 25 by 5 to get 5, and then 5 by 5 to get 1.

Here, 5 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 2400 is: 2^5 × 3 × 5^2.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 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), and (40, 60).

Negative factor pairs of 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), and (-40, -60).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, and 2400.
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 2400.
   
• Prime factorization: The method of expressing a number as the product of its prime factors. For example, the prime factorization of 2400 is 2^5 × 3 × 5^2.
   
• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 2400 are (1, 2400), (2, 1200), etc.
   
• Multiplication method: A method to find factor pairs by multiplying two numbers to get the original number. For example, 2 × 1200 = 2400.