Q: What are the factor combinations of the number 520,135?

 A:
Positive:   1 x 5201355 x 1040277 x 7430511 x 4728535 x 1486149 x 1061555 x 945777 x 6755193 x 2695245 x 2123385 x 1351539 x 965
Negative: -1 x -520135-5 x -104027-7 x -74305-11 x -47285-35 x -14861-49 x -10615-55 x -9457-77 x -6755-193 x -2695-245 x -2123-385 x -1351-539 x -965


How do I find the factor combinations of the number 520,135?

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 520,135, 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.

1 520,135
-1 -520,135

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 520,135.

Example:
1 x 520,135 = 520,135
and
-1 x -520,135 = 520,135
Notice both answers equal 520,135

With that explanation out of the way, let's continue. Next, we take the number 520,135 and divide it by 2:

520,135 ÷ 2 = 260,067.5

If the quotient is a whole number, then 2 and 260,067.5 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:

1 520,135
-1 -520,135

Now, we try dividing 520,135 by 3:

520,135 ÷ 3 = 173,378.3333

If the quotient is a whole number, then 3 and 173,378.3333 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:

1 520,135
-1 -520,135

Let's try dividing by 4:

520,135 ÷ 4 = 130,033.75

If the quotient is a whole number, then 4 and 130,033.75 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:

1 520,135
-1 520,135
Keep dividing by the next highest number until you cannot divide anymore.

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

15711354955771932453855399651,3512,1232,6956,7559,45710,61514,86147,28574,305104,027520,135
-1-5-7-11-35-49-55-77-193-245-385-539-965-1,351-2,123-2,695-6,755-9,457-10,615-14,861-47,285-74,305-104,027-520,135

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