Q: What are the factor combinations of the number 40,825,813?

 A:
Positive:   1 x 408258137 x 583225919 x 214872789 x 458717133 x 306961623 x 655311691 x 241433449 x 11837
Negative: -1 x -40825813-7 x -5832259-19 x -2148727-89 x -458717-133 x -306961-623 x -65531-1691 x -24143-3449 x -11837


How do I find the factor combinations of the number 40,825,813?

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 40,825,813, 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 40,825,813
-1 -40,825,813

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 40,825,813.

Example:
1 x 40,825,813 = 40,825,813
and
-1 x -40,825,813 = 40,825,813
Notice both answers equal 40,825,813

With that explanation out of the way, let's continue. Next, we take the number 40,825,813 and divide it by 2:

40,825,813 ÷ 2 = 20,412,906.5

If the quotient is a whole number, then 2 and 20,412,906.5 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 40,825,813
-1 -40,825,813

Now, we try dividing 40,825,813 by 3:

40,825,813 ÷ 3 = 13,608,604.3333

If the quotient is a whole number, then 3 and 13,608,604.3333 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 40,825,813
-1 -40,825,813

Let's try dividing by 4:

40,825,813 ÷ 4 = 10,206,453.25

If the quotient is a whole number, then 4 and 10,206,453.25 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 40,825,813
-1 40,825,813
Keep dividing by the next highest number until you cannot divide anymore.

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

1719891336231,6913,44911,83724,14365,531306,961458,7172,148,7275,832,25940,825,813
-1-7-19-89-133-623-1,691-3,449-11,837-24,143-65,531-306,961-458,717-2,148,727-5,832,259-40,825,813

More Examples

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