A:
Positive:
1 x 9722 x 4863 x 3244 x 2436 x 1629 x 10812 x 8118 x 5427 x 36
Negative:
-1 x -972-2 x -486-3 x -324-4 x -243-6 x -162-9 x -108-12 x -81-18 x -54-27 x -36
Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 972, it is easier to work with a table - it's called factoring from the outside in.
We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.
| 1 | 972 | |
| -1 | -972 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 972.
Example:
1 x 972 = 972
and
-1 x -972 = 972
Notice both answers equal 972
With that explanation out of the way, let's continue. Next, we take the number 972 and divide it by 2:
972 ÷ 2 = 486
If the quotient is a whole number, then 2 and 486 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 486 | 972 | |
| -1 | -2 | -486 | -972 |
Now, we try dividing 972 by 3:
972 ÷ 3 = 324
If the quotient is a whole number, then 3 and 324 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 3 | 324 | 486 | 972 | |
| -1 | -2 | -3 | -324 | -486 | -972 |
Let's try dividing by 4:
972 ÷ 4 = 243
If the quotient is a whole number, then 4 and 243 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 3 | 4 | 243 | 324 | 486 | 972 | |
| -1 | -2 | -3 | -4 | -243 | -324 | -486 | 972 |
If you did it right, you will end up with this table:
| 1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 27 | 36 | 54 | 81 | 108 | 162 | 243 | 324 | 486 | 972 |
| -1 | -2 | -3 | -4 | -6 | -9 | -12 | -18 | -27 | -36 | -54 | -81 | -108 | -162 | -243 | -324 | -486 | -972 |
Here are some more numbers to try:
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