Q: What are the factor combinations of the number 40,117?

 A:
Positive:   1 x 401177 x 573111 x 364777 x 521
Negative: -1 x -40117-7 x -5731-11 x -3647-77 x -521


How do I find the factor combinations of the number 40,117?

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 40,117, 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 40,117
-1 -40,117

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 40,117.

Example:
1 x 40,117 = 40,117
and
-1 x -40,117 = 40,117
Notice both answers equal 40,117

With that explanation out of the way, let's continue. Next, we take the number 40,117 and divide it by 2:

40,117 ÷ 2 = 20,058.5

If the quotient is a whole number, then 2 and 20,058.5 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 40,117
-1 -40,117

Now, we try dividing 40,117 by 3:

40,117 ÷ 3 = 13,372.3333

If the quotient is a whole number, then 3 and 13,372.3333 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 40,117
-1 -40,117

Let's try dividing by 4:

40,117 ÷ 4 = 10,029.25

If the quotient is a whole number, then 4 and 10,029.25 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 40,117
-1 40,117
Keep dividing by the next highest number until you cannot divide anymore.

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

1711775213,6475,73140,117
-1-7-11-77-521-3,647-5,731-40,117

More Examples

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