A:
Positive:
1 x 210842 x 105423 x 70284 x 52716 x 35147 x 301212 x 175714 x 150621 x 100428 x 75342 x 50284 x 251
Negative:
-1 x -21084-2 x -10542-3 x -7028-4 x -5271-6 x -3514-7 x -3012-12 x -1757-14 x -1506-21 x -1004-28 x -753-42 x -502-84 x -251
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 21,084, 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 | 21,084 | |
| -1 | -21,084 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 21,084.
Example:
1 x 21,084 = 21,084
and
-1 x -21,084 = 21,084
Notice both answers equal 21,084
With that explanation out of the way, let's continue. Next, we take the number 21,084 and divide it by 2:
21,084 ÷ 2 = 10,542
If the quotient is a whole number, then 2 and 10,542 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 | 10,542 | 21,084 | |
| -1 | -2 | -10,542 | -21,084 |
Now, we try dividing 21,084 by 3:
21,084 ÷ 3 = 7,028
If the quotient is a whole number, then 3 and 7,028 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 | 7,028 | 10,542 | 21,084 | |
| -1 | -2 | -3 | -7,028 | -10,542 | -21,084 |
Let's try dividing by 4:
21,084 ÷ 4 = 5,271
If the quotient is a whole number, then 4 and 5,271 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 | 5,271 | 7,028 | 10,542 | 21,084 | |
| -1 | -2 | -3 | -4 | -5,271 | -7,028 | -10,542 | 21,084 |
If you did it right, you will end up with this table:
| 1 | 2 | 3 | 4 | 6 | 7 | 12 | 14 | 21 | 28 | 42 | 84 | 251 | 502 | 753 | 1,004 | 1,506 | 1,757 | 3,012 | 3,514 | 5,271 | 7,028 | 10,542 | 21,084 |
| -1 | -2 | -3 | -4 | -6 | -7 | -12 | -14 | -21 | -28 | -42 | -84 | -251 | -502 | -753 | -1,004 | -1,506 | -1,757 | -3,012 | -3,514 | -5,271 | -7,028 | -10,542 | -21,084 |
Here are some more numbers to try:
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