Q: What are the factor combinations of the number 112,656?

 A:
Positive:   1 x 1126562 x 563283 x 375524 x 281646 x 187768 x 1408212 x 938816 x 704124 x 469448 x 2347
Negative: -1 x -112656-2 x -56328-3 x -37552-4 x -28164-6 x -18776-8 x -14082-12 x -9388-16 x -7041-24 x -4694-48 x -2347


How do I find the factor combinations of the number 112,656?

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 112,656, 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.

1 112,656
-1 -112,656

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 112,656.

Example:
1 x 112,656 = 112,656
and
-1 x -112,656 = 112,656
Notice both answers equal 112,656

With that explanation out of the way, let's continue. Next, we take the number 112,656 and divide it by 2:

112,656 ÷ 2 = 56,328

If the quotient is a whole number, then 2 and 56,328 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 56,328 112,656
-1 -2 -56,328 -112,656

Now, we try dividing 112,656 by 3:

112,656 ÷ 3 = 37,552

If the quotient is a whole number, then 3 and 37,552 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 37,552 56,328 112,656
-1 -2 -3 -37,552 -56,328 -112,656

Let's try dividing by 4:

112,656 ÷ 4 = 28,164

If the quotient is a whole number, then 4 and 28,164 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 28,164 37,552 56,328 112,656
-1 -2 -3 -4 -28,164 -37,552 -56,328 112,656
Keep dividing by the next highest number until you cannot divide anymore.

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

123468121624482,3474,6947,0419,38814,08218,77628,16437,55256,328112,656
-1-2-3-4-6-8-12-16-24-48-2,347-4,694-7,041-9,388-14,082-18,776-28,164-37,552-56,328-112,656

More Examples

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