Q: What are the factor combinations of the number 461,591?

 A:
Positive:   1 x 46159113 x 35507
Negative: -1 x -461591-13 x -35507


How do I find the factor combinations of the number 461,591?

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 461,591, 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.

1 461,591
-1 -461,591

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 461,591.

Example:
1 x 461,591 = 461,591
and
-1 x -461,591 = 461,591
Notice both answers equal 461,591

With that explanation out of the way, let's continue. Next, we take the number 461,591 and divide it by 2:

461,591 ÷ 2 = 230,795.5

If the quotient is a whole number, then 2 and 230,795.5 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:

1 461,591
-1 -461,591

Now, we try dividing 461,591 by 3:

461,591 ÷ 3 = 153,863.6667

If the quotient is a whole number, then 3 and 153,863.6667 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:

1 461,591
-1 -461,591

Let's try dividing by 4:

461,591 ÷ 4 = 115,397.75

If the quotient is a whole number, then 4 and 115,397.75 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:

1 461,591
-1 461,591
Keep dividing by the next highest number until you cannot divide anymore.

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

11335,507461,591
-1-13-35,507-461,591

More Examples

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