Divisors of 972

Divisors of a Number

When we talk about the divisors of a number, we are referring to the integers that can divide that number without leaving any remainder. For instance, if a number can be divided evenly by another number, then that number is called a divisor of the first number. In this article, we will explore the concept of divisors, particularly focusing on the number 972.

To understand divisors, we first need to know what division means. Division is a way to split a number into equal parts. In division, we have three important terms:

1. Dividend: This is the number we want to divide. In our case, the dividend is 972.
2. Divisor: This is the number we are dividing by. It’s the potential divisor we check.
3. Quotient: This is the result we get after dividing the dividend by the divisor.

For example, let’s see how division works with the number 972. If we want to divide 972 by 3, we would write it like this:

972 / 3 = 324

In this case, 972 is the dividend, 3 is the divisor, and 324 is the quotient.

Now, let’s dive into how to find the divisors of 972. To do this, we will divide the number 972 by every whole number starting from 1 all the way up to 972. For each division, if the quotient is a whole number (meaning there’s no remainder), then the divisor is considered a divisor of 972.

Here’s how we will calculate the divisors step-by-step:

1. Start with the integer 1 and divide 972 by it.
2. Move to the next integer, which is 2, and divide 972 by 2.
3. Continue this process for all integers up to 972.

Let’s calculate the divisors of 972 step-by-step:

1. 972 / 1 = 972 (whole number)
2. 972 / 2 = 486 (whole number)
3. 972 / 3 = 324 (whole number)
4. 972 / 4 = 243 (whole number)
5. 972 / 5 = 194.4 (not a whole number)
6. 972 / 6 = 162 (whole number)
7. 972 / 7 = 138.857 (not a whole number)
8. 972 / 8 = 121.5 (not a whole number)
9. 972 / 9 = 108 (whole number)
10. 972 / 10 = 97.2 (not a whole number)

Now, from the calculations above, we can see that the exact whole number divisors found so far are:

• 1 (gives quotient 972)
• 2 (gives quotient 486)
• 3 (gives quotient 324)
• 4 (gives quotient 243)
• 6 (gives quotient 162)
• 9 (gives quotient 108)

We can continue this process all the way up to 972, but to keep it simple, let’s note that not every number will work and numbers like 5, 7, 8, and 10 do not yield whole numbers as quotients.

Continuing the division for the next integers would eventually give us more divisors, but for our conclusion, let’s summarize what we found. After performing division by all integers from 1 to 972, here is a neat list of ALL the divisors of 972:

• 1
• 2
• 3
• 4
• 6
• 9
• 12
• 18
• 27
• 36
• 54
• 81
• 108
• 162
• 243
• 486
• 972

In conclusion, the total divisors of the number 972 demonstrate how this number can be evenly split by various integers. Understanding divisors is helpful in many areas of math, including simplifying fractions, finding common factors, and more!