Divisors of 90

Divisors of a number are the whole numbers that can divide that number without leaving a remainder. Understanding divisors is important in various areas of mathematics, such as simplifying fractions, finding common factors, and working with ratios. In this article, we will explore the divisors of the number 90, showing you how to find them step by step.

To understand divisors, you also need to know a little about division. Division is when a number is split into equal parts. Let’s break down the terms:

• Dividend: This is the number you want to divide. In our example with the number 90, it will be the dividend.
• Divisor: This is the number by which you divide the dividend. We will use 1, 2, 3, and so on as our divisors.
• Quotient: This is the result you get when you divide the dividend by the divisor.

For example, with the number 90:
If you divide 90 by 1, you have:
90 / 1 = 90
Here, 90 is the dividend, 1 is the divisor, and 90 is the quotient.

Now, let’s find the divisors of 90. We will do this by dividing 90 by every integer starting from 1 up to 90 itself.

1. Start with the number 1:
   90 / 1 = 90 (whole number)

2. Next, try 2:
   90 / 2 = 45 (whole number)

3. Now, try 3:
   90 / 3 = 30 (whole number)

4. Move to 4:
   90 / 4 = 22.5 (not a whole number)

5. Next is 5:
   90 / 5 = 18 (whole number)

6. Try 6:
   90 / 6 = 15 (whole number)

7. Next, we’ll try 7:
   90 / 7 = 12.857 (not a whole number)

8. Now, let’s check 8:
   90 / 8 = 11.25 (not a whole number)

9. Try 9:
   90 / 9 = 10 (whole number)

10. Finally, check 10:
    90 / 10 = 9 (whole number)

After trying these numbers, we find the divisors that give us whole numbers. They are:

1. 90 / 1 = 90 (divisor: 1)
2. 90 / 2 = 45 (divisor: 2)
3. 90 / 3 = 30 (divisor: 3)
4. 90 / 5 = 18 (divisor: 5)
5. 90 / 6 = 15 (divisor: 6)
6. 90 / 9 = 10 (divisor: 9)
7. 90 / 10 = 9 (divisor: 10)

We can see that the numbers that can divide 90 evenly are: 1, 2, 3, 5, 6, 9, and 10.

To list all the divisors of 90 clearly, they are as follows:

• 1
• 2
• 3
• 5
• 6
• 9
• 10
• 15
• 18
• 30
• 45
• 90

In conclusion, the divisors of the number 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Each of these numbers, when used to divide 90, results in a whole number, which is the key characteristic of divisors. Understanding how to find divisors can help in many areas of math, making it an important concept to master!