Q: What are the factor combinations of the number 398,473,595?

 A:
Positive:   1 x 3984735955 x 7969471913 x 3065181565 x 6130363113 x 3526315565 x 7052631469 x 2712557345 x 54251
Negative: -1 x -398473595-5 x -79694719-13 x -30651815-65 x -6130363-113 x -3526315-565 x -705263-1469 x -271255-7345 x -54251


How do I find the factor combinations of the number 398,473,595?

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 398,473,595, 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.

1 398,473,595
-1 -398,473,595

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 398,473,595.

Example:
1 x 398,473,595 = 398,473,595
and
-1 x -398,473,595 = 398,473,595
Notice both answers equal 398,473,595

With that explanation out of the way, let's continue. Next, we take the number 398,473,595 and divide it by 2:

398,473,595 ÷ 2 = 199,236,797.5

If the quotient is a whole number, then 2 and 199,236,797.5 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:

1 398,473,595
-1 -398,473,595

Now, we try dividing 398,473,595 by 3:

398,473,595 ÷ 3 = 132,824,531.6667

If the quotient is a whole number, then 3 and 132,824,531.6667 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:

1 398,473,595
-1 -398,473,595

Let's try dividing by 4:

398,473,595 ÷ 4 = 99,618,398.75

If the quotient is a whole number, then 4 and 99,618,398.75 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:

1 398,473,595
-1 398,473,595
Keep dividing by the next highest number until you cannot divide anymore.

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

1513651135651,4697,34554,251271,255705,2633,526,3156,130,36330,651,81579,694,719398,473,595
-1-5-13-65-113-565-1,469-7,345-54,251-271,255-705,263-3,526,315-6,130,363-30,651,815-79,694,719-398,473,595

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