Q: What are the factor combinations of the number 40,944,025?

 A:
Positive:   1 x 409440255 x 818880523 x 178017525 x 163776131 x 1320775115 x 356035155 x 264155575 x 71207713 x 57425775 x 528312297 x 178253565 x 11485
Negative: -1 x -40944025-5 x -8188805-23 x -1780175-25 x -1637761-31 x -1320775-115 x -356035-155 x -264155-575 x -71207-713 x -57425-775 x -52831-2297 x -17825-3565 x -11485


How do I find the factor combinations of the number 40,944,025?

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 40,944,025, 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 40,944,025
-1 -40,944,025

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 40,944,025.

Example:
1 x 40,944,025 = 40,944,025
and
-1 x -40,944,025 = 40,944,025
Notice both answers equal 40,944,025

With that explanation out of the way, let's continue. Next, we take the number 40,944,025 and divide it by 2:

40,944,025 ÷ 2 = 20,472,012.5

If the quotient is a whole number, then 2 and 20,472,012.5 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 40,944,025
-1 -40,944,025

Now, we try dividing 40,944,025 by 3:

40,944,025 ÷ 3 = 13,648,008.3333

If the quotient is a whole number, then 3 and 13,648,008.3333 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 40,944,025
-1 -40,944,025

Let's try dividing by 4:

40,944,025 ÷ 4 = 10,236,006.25

If the quotient is a whole number, then 4 and 10,236,006.25 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 40,944,025
-1 40,944,025
Keep dividing by the next highest number until you cannot divide anymore.

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

152325311151555757137752,2973,56511,48517,82552,83157,42571,207264,155356,0351,320,7751,637,7611,780,1758,188,80540,944,025
-1-5-23-25-31-115-155-575-713-775-2,297-3,565-11,485-17,825-52,831-57,425-71,207-264,155-356,035-1,320,775-1,637,761-1,780,175-8,188,805-40,944,025

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