Q: What are the factor combinations of the number 9,821?

 A:
Positive:   1 x 98217 x 140323 x 42761 x 161
Negative: -1 x -9821-7 x -1403-23 x -427-61 x -161


How do I find the factor combinations of the number 9,821?

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 9,821, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

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 9,821
-1 -9,821

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 9,821.

Example:
1 x 9,821 = 9,821
and
-1 x -9,821 = 9,821
Notice both answers equal 9,821

With that explanation out of the way, let's continue. Next, we take the number 9,821 and divide it by 2:

9,821 ÷ 2 = 4,910.5

If the quotient is a whole number, then 2 and 4,910.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 9,821
-1 -9,821

Now, we try dividing 9,821 by 3:

9,821 ÷ 3 = 3,273.6667

If the quotient is a whole number, then 3 and 3,273.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 9,821
-1 -9,821

Let's try dividing by 4:

9,821 ÷ 4 = 2,455.25

If the quotient is a whole number, then 4 and 2,455.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 9,821
-1 9,821
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1723611614271,4039,821
-1-7-23-61-161-427-1,403-9,821

More Examples

Here are some more numbers to try:

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