Q: What are the factor combinations of the number 27,807,017?

 A:
Positive:   1 x 278070177 x 397243137 x 751541101 x 275317259 x 107363707 x 393311063 x 261593737 x 7441
Negative: -1 x -27807017-7 x -3972431-37 x -751541-101 x -275317-259 x -107363-707 x -39331-1063 x -26159-3737 x -7441


How do I find the factor combinations of the number 27,807,017?

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 27,807,017, 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 27,807,017
-1 -27,807,017

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 27,807,017.

Example:
1 x 27,807,017 = 27,807,017
and
-1 x -27,807,017 = 27,807,017
Notice both answers equal 27,807,017

With that explanation out of the way, let's continue. Next, we take the number 27,807,017 and divide it by 2:

27,807,017 ÷ 2 = 13,903,508.5

If the quotient is a whole number, then 2 and 13,903,508.5 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 27,807,017
-1 -27,807,017

Now, we try dividing 27,807,017 by 3:

27,807,017 ÷ 3 = 9,269,005.6667

If the quotient is a whole number, then 3 and 9,269,005.6667 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 27,807,017
-1 -27,807,017

Let's try dividing by 4:

27,807,017 ÷ 4 = 6,951,754.25

If the quotient is a whole number, then 4 and 6,951,754.25 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 27,807,017
-1 27,807,017
Keep dividing by the next highest number until you cannot divide anymore.

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

17371012597071,0633,7377,44126,15939,331107,363275,317751,5413,972,43127,807,017
-1-7-37-101-259-707-1,063-3,737-7,441-26,159-39,331-107,363-275,317-751,541-3,972,431-27,807,017

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