Q: What are the factor combinations of the number 46,123,259?

 A:
Positive:   1 x 461232597 x 658903713 x 354794349 x 94129161 x 75611991 x 506849427 x 108017637 x 72407793 x 581631187 x 388572989 x 154315551 x 8309
Negative: -1 x -46123259-7 x -6589037-13 x -3547943-49 x -941291-61 x -756119-91 x -506849-427 x -108017-637 x -72407-793 x -58163-1187 x -38857-2989 x -15431-5551 x -8309


How do I find the factor combinations of the number 46,123,259?

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 46,123,259, 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 46,123,259
-1 -46,123,259

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 46,123,259.

Example:
1 x 46,123,259 = 46,123,259
and
-1 x -46,123,259 = 46,123,259
Notice both answers equal 46,123,259

With that explanation out of the way, let's continue. Next, we take the number 46,123,259 and divide it by 2:

46,123,259 ÷ 2 = 23,061,629.5

If the quotient is a whole number, then 2 and 23,061,629.5 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 46,123,259
-1 -46,123,259

Now, we try dividing 46,123,259 by 3:

46,123,259 ÷ 3 = 15,374,419.6667

If the quotient is a whole number, then 3 and 15,374,419.6667 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 46,123,259
-1 -46,123,259

Let's try dividing by 4:

46,123,259 ÷ 4 = 11,530,814.75

If the quotient is a whole number, then 4 and 11,530,814.75 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 46,123,259
-1 46,123,259
Keep dividing by the next highest number until you cannot divide anymore.

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

17134961914276377931,1872,9895,5518,30915,43138,85758,16372,407108,017506,849756,119941,2913,547,9436,589,03746,123,259
-1-7-13-49-61-91-427-637-793-1,187-2,989-5,551-8,309-15,431-38,857-58,163-72,407-108,017-506,849-756,119-941,291-3,547,943-6,589,037-46,123,259

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