Divisors of 27

Divisors of a number are the integers that can divide that number without leaving a remainder. For example, if a number is divided evenly, the integers that accomplish this are called divisors. Understanding divisors is important because it helps in various areas of mathematics, including fractions, simplification, and finding factors of numbers. In this article, we will explore the divisors of the number 27.

To begin, let’s review the concept of division. When we divide one number by another, we use specific terms. The first number is called the "dividend" (the number we are dividing). The second number is called the "divisor" (the number we are dividing by), and the result of the division is called the "quotient."

For example, in the division 27 / 3 = 9:

• 27 is the dividend (the number we start with).
• 3 is the divisor (the number we are dividing by).
• 9 is the quotient (the result of the division).

Next, let’s calculate the divisors of 27. To find out which integers can divide 27, we will divide the number 27 by every integer from 1 up to 27 itself.

Here’s how to do this step-by-step:

1. Start with the number 1.
2. Increase the number by 1 each time (2, 3, 4, and so on) until you reach 27.
3. Divide 27 by each of these numbers.
4. Check if the result (quotient) is a whole number. If it is, then that number is a divisor of 27.

Now let’s go through the calculations:

1. 27 / 1 = 27 (whole number, divisor)
2. 27 / 2 = 13.5 (not a whole number)
3. 27 / 3 = 9 (whole number, divisor)
4. 27 / 4 = 6.75 (not a whole number)
5. 27 / 5 = 5.4 (not a whole number)
6. 27 / 6 = 4.5 (not a whole number)
7. 27 / 7 = 3.857 (not a whole number)
8. 27 / 8 = 3.375 (not a whole number)
9. 27 / 9 = 3 (whole number, divisor)
10. 27 / 10 = 2.7 (not a whole number)
11. 27 / 11 = 2.454 (not a whole number)
12. 27 / 12 = 2.25 (not a whole number)
13. 27 / 13 = 2.076 (not a whole number)
14. 27 / 14 = 1.928 (not a whole number)
15. 27 / 15 = 1.8 (not a whole number)
16. 27 / 16 = 1.6875 (not a whole number)
17. 27 / 17 = 1.588 (not a whole number)
18. 27 / 18 = 1.5 (not a whole number)
19. 27 / 19 = 1.421 (not a whole number)
20. 27 / 20 = 1.35 (not a whole number)
21. 27 / 21 = 1.2857 (not a whole number)
22. 27 / 22 = 1.227 (not a whole number)
23. 27 / 23 = 1.174 (not a whole number)
24. 27 / 24 = 1.125 (not a whole number)
25. 27 / 25 = 1.08 (not a whole number)
26. 27 / 26 = 1.038 (not a whole number)
27. 27 / 27 = 1 (whole number, divisor)

Now, we will list the results showing which divisions produced whole numbers. The divisors of 27 are:

1. 1 (27 / 1 = 27)
2. 3 (27 / 3 = 9)
3. 9 (27 / 9 = 3)
4. 27 (27 / 27 = 1)

In conclusion, the complete list of divisors of the number 27 is:

1, 3, 9, 27

These numbers can divide 27 evenly without leaving a remainder. Understanding divisors is a fundamental concept that lays the groundwork for more advanced math topics.