Q: What are the factor combinations of the number 515,422,565?

 A:
Positive:   1 x 5154225655 x 1030845137 x 7363179535 x 14726359751 x 6863153755 x 1372635257 x 9804519609 x 26285
Negative: -1 x -515422565-5 x -103084513-7 x -73631795-35 x -14726359-751 x -686315-3755 x -137263-5257 x -98045-19609 x -26285


How do I find the factor combinations of the number 515,422,565?

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 515,422,565, 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.

1 515,422,565
-1 -515,422,565

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 515,422,565.

Example:
1 x 515,422,565 = 515,422,565
and
-1 x -515,422,565 = 515,422,565
Notice both answers equal 515,422,565

With that explanation out of the way, let's continue. Next, we take the number 515,422,565 and divide it by 2:

515,422,565 ÷ 2 = 257,711,282.5

If the quotient is a whole number, then 2 and 257,711,282.5 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:

1 515,422,565
-1 -515,422,565

Now, we try dividing 515,422,565 by 3:

515,422,565 ÷ 3 = 171,807,521.6667

If the quotient is a whole number, then 3 and 171,807,521.6667 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:

1 515,422,565
-1 -515,422,565

Let's try dividing by 4:

515,422,565 ÷ 4 = 128,855,641.25

If the quotient is a whole number, then 4 and 128,855,641.25 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:

1 515,422,565
-1 515,422,565
Keep dividing by the next highest number until you cannot divide anymore.

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

157357513,7555,25719,60926,28598,045137,263686,31514,726,35973,631,795103,084,513515,422,565
-1-5-7-35-751-3,755-5,257-19,609-26,285-98,045-137,263-686,315-14,726,359-73,631,795-103,084,513-515,422,565

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