Q: What are the factor combinations of the number 413,320,427?

 A:
Positive:   1 x 41332042713 x 3179387931 x 13332917169 x 2445683403 x 10256095239 x 78893
Negative: -1 x -413320427-13 x -31793879-31 x -13332917-169 x -2445683-403 x -1025609-5239 x -78893


How do I find the factor combinations of the number 413,320,427?

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 413,320,427, 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.

1 413,320,427
-1 -413,320,427

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 413,320,427.

Example:
1 x 413,320,427 = 413,320,427
and
-1 x -413,320,427 = 413,320,427
Notice both answers equal 413,320,427

With that explanation out of the way, let's continue. Next, we take the number 413,320,427 and divide it by 2:

413,320,427 ÷ 2 = 206,660,213.5

If the quotient is a whole number, then 2 and 206,660,213.5 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:

1 413,320,427
-1 -413,320,427

Now, we try dividing 413,320,427 by 3:

413,320,427 ÷ 3 = 137,773,475.6667

If the quotient is a whole number, then 3 and 137,773,475.6667 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:

1 413,320,427
-1 -413,320,427

Let's try dividing by 4:

413,320,427 ÷ 4 = 103,330,106.75

If the quotient is a whole number, then 4 and 103,330,106.75 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:

1 413,320,427
-1 413,320,427
Keep dividing by the next highest number until you cannot divide anymore.

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

113311694035,23978,8931,025,6092,445,68313,332,91731,793,879413,320,427
-1-13-31-169-403-5,239-78,893-1,025,609-2,445,683-13,332,917-31,793,879-413,320,427

More Examples

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