Divisors of 231

Divisors of a number are the numbers that can be multiplied together to produce that number. In simpler terms, if you can divide a number evenly without leaving a remainder, then that number is called a divisor of the original number. This article aims to explain what divisors are and how to find them, specifically using the example of the number 231.

To understand divisors better, we need to get familiar with the concept of division. Division is a process used to split a number into equal parts. When we divide, we have three important terms:

1. Dividend: This is the number we want to divide. For our example, the dividend is 231.
2. Divisor: This is the number by which we are dividing the dividend. It will change as we check different integers.
3. Quotient: This is the result we get after performing the division. If the division is exact (no remainder), we find a divisor.

The formula for division can be shown like this:

Dividend / Divisor = Quotient

For example, if we divide 231 by 3, we can see it as:

231 / 3 = 77

In this case, 231 is the dividend, 3 is the divisor, and 77 is the quotient. Since 77 is a whole number, we can say that 3 is a divisor of 231.

Now let’s find all the divisors of the number 231. We will test every integer from 1 up to 231 to see if it divides evenly into 231. Here’s a step-by-step guide on how to do this:

1. Start with 1 and go up to 231.
2. For each integer ( x ) from 1 to 231, calculate 231 / ( x ).
3. If the result (quotient) is a whole number (meaning there’s no remainder), then ( x ) is a divisor of 231.

Let’s perform the calculations for the integers from 1 to 10:

1. 231 / 1 = 231 (whole number, divisor)
2. 231 / 2 = 115.5 (not a whole number)
3. 231 / 3 = 77 (whole number, divisor)
4. 231 / 4 = 57.75 (not a whole number)
5. 231 / 5 = 46.2 (not a whole number)
6. 231 / 6 = 38.5 (not a whole number)
7. 231 / 7 = 33 (whole number, divisor)
8. 231 / 8 = 28.875 (not a whole number)
9. 231 / 9 = 25.6667 (not a whole number)
10. 231 / 10 = 23.1 (not a whole number)

After checking all these numbers, we can compile a list of the numbers we found that are divisors of 231. The divisors we discovered from our calculations so far are:

1. 1
2. 3
3. 7

To get the full list of divisors, we would continue this process up to 231. However, based on the examples presented, we already know that we’ve found a few divisors.

The complete list of all the divisors of 231 is:

• 1
• 3
• 7
• 11
• 21
• 33
• 77
• 231

In summary, the divisors of a number are the integers that divide it evenly without leaving a remainder. For the number 231, the divisors include 1, 3, 7, 11, 21, 33, 77, and 231 itself.