Q: What are the factor combinations of the number 361,513?

 A:
Positive:   1 x 36151319 x 1902753 x 6821359 x 1007
Negative: -1 x -361513-19 x -19027-53 x -6821-359 x -1007


How do I find the factor combinations of the number 361,513?

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 361,513, 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.

1 361,513
-1 -361,513

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 361,513.

Example:
1 x 361,513 = 361,513
and
-1 x -361,513 = 361,513
Notice both answers equal 361,513

With that explanation out of the way, let's continue. Next, we take the number 361,513 and divide it by 2:

361,513 ÷ 2 = 180,756.5

If the quotient is a whole number, then 2 and 180,756.5 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:

1 361,513
-1 -361,513

Now, we try dividing 361,513 by 3:

361,513 ÷ 3 = 120,504.3333

If the quotient is a whole number, then 3 and 120,504.3333 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:

1 361,513
-1 -361,513

Let's try dividing by 4:

361,513 ÷ 4 = 90,378.25

If the quotient is a whole number, then 4 and 90,378.25 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:

1 361,513
-1 361,513
Keep dividing by the next highest number until you cannot divide anymore.

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

119533591,0076,82119,027361,513
-1-19-53-359-1,007-6,821-19,027-361,513

More Examples

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