Q: What are the factor combinations of the number 520,429?

 A:
Positive:   1 x 5204297 x 7434713 x 4003319 x 2739143 x 1210349 x 1062191 x 5719133 x 3913247 x 2107301 x 1729559 x 931637 x 817
Negative: -1 x -520429-7 x -74347-13 x -40033-19 x -27391-43 x -12103-49 x -10621-91 x -5719-133 x -3913-247 x -2107-301 x -1729-559 x -931-637 x -817


How do I find the factor combinations of the number 520,429?

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 520,429, 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.

1 520,429
-1 -520,429

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 520,429.

Example:
1 x 520,429 = 520,429
and
-1 x -520,429 = 520,429
Notice both answers equal 520,429

With that explanation out of the way, let's continue. Next, we take the number 520,429 and divide it by 2:

520,429 ÷ 2 = 260,214.5

If the quotient is a whole number, then 2 and 260,214.5 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:

1 520,429
-1 -520,429

Now, we try dividing 520,429 by 3:

520,429 ÷ 3 = 173,476.3333

If the quotient is a whole number, then 3 and 173,476.3333 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:

1 520,429
-1 -520,429

Let's try dividing by 4:

520,429 ÷ 4 = 130,107.25

If the quotient is a whole number, then 4 and 130,107.25 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:

1 520,429
-1 520,429
Keep dividing by the next highest number until you cannot divide anymore.

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

1713194349911332473015596378179311,7292,1073,9135,71910,62112,10327,39140,03374,347520,429
-1-7-13-19-43-49-91-133-247-301-559-637-817-931-1,729-2,107-3,913-5,719-10,621-12,103-27,391-40,033-74,347-520,429

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