Divisors of 400

When we talk about the divisors of a number, we are referring to the numbers that can be multiplied together to give that original number. In simpler words, a divisor is a number that divides another number evenly, without leaving any remainder. In this article, we will explore what divisors are, how to find them, and we will specifically look at the divisors of the number 400.

To understand divisors better, we first need to know about division. Division is separating or distributing a number (called the dividend) into equal parts or groups. The number we are dividing by is called the divisor, and the result we get from division is known as the quotient.

For example, let’s consider the number 400. In the division expression “400 / 1 = 400,” the number 400 is the dividend, 1 is the divisor, and the result (400) is the quotient.

Now, let’s calculate the divisors of 400 step by step. The method we will use is quite straightforward: we will divide 400 by every whole number starting from 1 up to 400 itself. If the result is a whole number (an integer), then the divisor is valid.

1. Starting with 1:

   • 400 / 1 = 400 (whole number)

2. Then 2:

   • 400 / 2 = 200 (whole number)

3. Next, 3:

   • 400 / 3 = 133.33 (not a whole number)

4. Then 4:

   • 400 / 4 = 100 (whole number)

5. Next, 5:

   • 400 / 5 = 80 (whole number)

6. Then 6:

   • 400 / 6 = 66.67 (not a whole number)

7. Next, 7:

   • 400 / 7 = 57.14 (not a whole number)

8. Then 8:

   • 400 / 8 = 50 (whole number)

9. Next, 9:

   • 400 / 9 = 44.44 (not a whole number)
10. Then 10:
    • 400 / 10 = 40 (whole number)

Continuing beyond this point, for 11 and further, we will find that there are still more divisors. However, for brevity, we will summarize that the further divisions yield whole numbers sporadically, but we can confidently identify the first ten valid divisors.

Here is a detailed list showing the valid divisors from our calculations:

• 400 / 1 = 400
• 400 / 2 = 200
• 400 / 4 = 100
• 400 / 5 = 80
• 400 / 8 = 50
• 400 / 10 = 40

Continuing this process, you can find more divisors like 16, 25, 20, etc.

In conclusion, the complete list of divisors of 400 includes:

1. 1
2. 2
3. 4
4. 5
5. 8
6. 10
7. 16
8. 20
9. 25
10. 40
11. 50
12. 80
13. 100
14. 200
15. 400

These are all the numbers that can evenly divide 400, demonstrating how divisors work. Understanding divisors helps in many areas of math and can be very useful in various applications!