Divisors of a number are the integers that can be evenly divided into that number. In simpler words, if you can divide a number by another number and the result is a whole number (not a fraction), then the second number is a divisor of the first number. This article will explain what divisors are, how to find them, and provide an example using the number 36.
To understand divisors better, let’s take a closer look at division. When we divide one number by another, we have three important terms:
- Dividend: The number we want to divide.
- Divisor: The number we are dividing by.
- Quotient: The result of the division.
For example, in the equation 36 / 6 = 6, 36 is the dividend, 6 is the divisor, and the quotient is also 6.
Now, let’s learn how to calculate the divisors of the number 36. To do this, we will divide 36 by every whole number starting at 1 and going up to 36. If the result is a whole number, that divisor is a divisor of 36.
Here’s how you do it step-by-step:
- Start with the number 1.
- Divide 36 by 1:
36 / 1 = 36 (whole number) - Next, divide 36 by 2:
36 / 2 = 18 (whole number) - Then, divide 36 by 3:
36 / 3 = 12 (whole number) - Now, divide 36 by 4:
36 / 4 = 9 (whole number) - Next, divide 36 by 5:
36 / 5 = 7.2 (not a whole number) - Now, divide 36 by 6:
36 / 6 = 6 (whole number) - Next, divide 36 by 7:
36 / 7 = 5.14 (not a whole number) - Next, divide 36 by 8:
36 / 8 = 4.5 (not a whole number) - Finally, divide 36 by 9:
36 / 9 = 4 (whole number)
Continuing this process, we can divide 36 by the next numbers but will only show the results for numbers up to 10. The whole numbers we have found so far that are divisors of 36 are:
- 36 / 1 = 36 (whole number)
- 36 / 2 = 18 (whole number)
- 36 / 3 = 12 (whole number)
- 36 / 4 = 9 (whole number)
- 36 / 5 = 7.2 (not a whole number)
- 36 / 6 = 6 (whole number)
- 36 / 7 = 5.14 (not a whole number)
- 36 / 8 = 4.5 (not a whole number)
- 36 / 9 = 4 (whole number)
- 36 / 10 = 3.6 (not a whole number)
Now, moving on to more potential divisors, we find:
- 36 / 11 = 3.27 (not a whole number)
- 36 / 12 = 3 (whole number)
- 36 / 13 = 2.77 (not a whole number)
- 36 / 14 = 2.57 (not a whole number)
- 36 / 15 = 2.4 (not a whole number)
- 36 / 16 = 2.25 (not a whole number)
- 36 / 17 = 2.12 (not a whole number)
- 36 / 18 = 2 (whole number)
- 36 / 19 = 1.89 (not a whole number)
- 36 / 20 = 1.8 (not a whole number)
- and so on, until we reach 36
The full list of divisors for the number 36, including those we calculated above, is:
1, 2, 3, 4, 6, 9, 12, 18, 36
In conclusion, the divisors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36.
These numbers can divide 36 evenly without leaving any remainder, making them its divisors!