Q: What are the factor combinations of the number 111,635?

 A:
Positive:   1 x 1116355 x 2232783 x 1345269 x 415
Negative: -1 x -111635-5 x -22327-83 x -1345-269 x -415


How do I find the factor combinations of the number 111,635?

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 111,635, 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.

1 111,635
-1 -111,635

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 111,635.

Example:
1 x 111,635 = 111,635
and
-1 x -111,635 = 111,635
Notice both answers equal 111,635

With that explanation out of the way, let's continue. Next, we take the number 111,635 and divide it by 2:

111,635 ÷ 2 = 55,817.5

If the quotient is a whole number, then 2 and 55,817.5 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:

1 111,635
-1 -111,635

Now, we try dividing 111,635 by 3:

111,635 ÷ 3 = 37,211.6667

If the quotient is a whole number, then 3 and 37,211.6667 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:

1 111,635
-1 -111,635

Let's try dividing by 4:

111,635 ÷ 4 = 27,908.75

If the quotient is a whole number, then 4 and 27,908.75 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:

1 111,635
-1 111,635
Keep dividing by the next highest number until you cannot divide anymore.

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

15832694151,34522,327111,635
-1-5-83-269-415-1,345-22,327-111,635

More Examples

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