When we talk about the divisors of a number, we mean the whole numbers that can divide that number without leaving a remainder. For example, if we take the number 135, its divisors are the numbers you can divide 135 by to get a whole number. This article will help you understand what divisors are, how to find them, and give you a complete list of the divisors of the number 135.
To understand divisors better, we first need to know what division is. Division is a way to split a number into equal parts. In division, we have three important terms:
- Dividend: This is the number we want to divide. In our case, the dividend is 135.
- Divisor: This is the number we use to divide the dividend. We will test each whole number to see if it divides 135.
- Quotient: This is the result of the division. It tells us how many times the divisor fits into the dividend.
For example, when we divide 135 by 1, we can write it like this:
135 / 1 = 135
In this case, 135 is the dividend, 1 is the divisor, and 135 is the quotient.
Now let’s find the divisors of 135 step-by-step. We will divide 135 by every whole number starting from 1 up to 135. The divisors will be those numbers that result in a whole number (meaning no remainder).
Here’s how we do it:
-
Start with the number 1:
135 / 1 = 135 (This is a whole number) -
Next, try 2:
135 / 2 = 67.5 (Not a whole number) -
Now try 3:
135 / 3 = 45 (This is a whole number) -
Next is 4:
135 / 4 = 33.75 (Not a whole number) -
Try 5:
135 / 5 = 27 (This is a whole number) -
Now let’s check 6:
135 / 6 = 22.5 (Not a whole number) -
Next, try 7:
135 / 7 = 19.285714… (Not a whole number) -
Now let’s do 8:
135 / 8 = 16.875 (Not a whole number) -
Check 9:
135 / 9 = 15 (This is a whole number) - Finally, try 10:
135 / 10 = 13.5 (Not a whole number)
We’ve found some divisors so far! Let’s recap the calculations that resulted in whole numbers:
- 135 / 1 = 135 (divisor: 1)
- 135 / 3 = 45 (divisor: 3)
- 135 / 5 = 27 (divisor: 5)
- 135 / 9 = 15 (divisor: 9)
We can continue this process until we reach 135, but for brevity, we can note that the divisors of 135 include:
- 135 / 15 = 9 (divisor: 15)
- 135 / 27 = 5 (divisor: 27)
- 135 / 45 = 3 (divisor: 45)
- 135 / 135 = 1 (divisor: 135)
Now, let’s list all the divisors of 135 in a neat format. The complete list of divisors is:
1, 3, 5, 9, 15, 27, 45, 135
In conclusion, the divisors of the number 135 are 1, 3, 5, 9, 15, 27, 45, and 135. These values are useful in various areas of mathematics, including simplifying fractions and understanding the relationships between numbers.