Q: What are the factor combinations of the number 7,032,109?

 A:
Positive:   1 x 70321097 x 100458719 x 37011137 x 190057133 x 52873259 x 27151703 x 100031429 x 4921
Negative: -1 x -7032109-7 x -1004587-19 x -370111-37 x -190057-133 x -52873-259 x -27151-703 x -10003-1429 x -4921


How do I find the factor combinations of the number 7,032,109?

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 7,032,109, 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 7,032,109
-1 -7,032,109

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 7,032,109.

Example:
1 x 7,032,109 = 7,032,109
and
-1 x -7,032,109 = 7,032,109
Notice both answers equal 7,032,109

With that explanation out of the way, let's continue. Next, we take the number 7,032,109 and divide it by 2:

7,032,109 ÷ 2 = 3,516,054.5

If the quotient is a whole number, then 2 and 3,516,054.5 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 7,032,109
-1 -7,032,109

Now, we try dividing 7,032,109 by 3:

7,032,109 ÷ 3 = 2,344,036.3333

If the quotient is a whole number, then 3 and 2,344,036.3333 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 7,032,109
-1 -7,032,109

Let's try dividing by 4:

7,032,109 ÷ 4 = 1,758,027.25

If the quotient is a whole number, then 4 and 1,758,027.25 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 7,032,109
-1 7,032,109
Keep dividing by the next highest number until you cannot divide anymore.

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

1719371332597031,4294,92110,00327,15152,873190,057370,1111,004,5877,032,109
-1-7-19-37-133-259-703-1,429-4,921-10,003-27,151-52,873-190,057-370,111-1,004,587-7,032,109

More Examples

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