Q: What are the factor combinations of the number 3,520,513?

 A:
Positive:   1 x 352051317 x 20708929 x 12139737 x 95149193 x 18241493 x 7141629 x 55971073 x 3281
Negative: -1 x -3520513-17 x -207089-29 x -121397-37 x -95149-193 x -18241-493 x -7141-629 x -5597-1073 x -3281


How do I find the factor combinations of the number 3,520,513?

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 3,520,513, 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 3,520,513
-1 -3,520,513

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 3,520,513.

Example:
1 x 3,520,513 = 3,520,513
and
-1 x -3,520,513 = 3,520,513
Notice both answers equal 3,520,513

With that explanation out of the way, let's continue. Next, we take the number 3,520,513 and divide it by 2:

3,520,513 ÷ 2 = 1,760,256.5

If the quotient is a whole number, then 2 and 1,760,256.5 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 3,520,513
-1 -3,520,513

Now, we try dividing 3,520,513 by 3:

3,520,513 ÷ 3 = 1,173,504.3333

If the quotient is a whole number, then 3 and 1,173,504.3333 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 3,520,513
-1 -3,520,513

Let's try dividing by 4:

3,520,513 ÷ 4 = 880,128.25

If the quotient is a whole number, then 4 and 880,128.25 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 3,520,513
-1 3,520,513
Keep dividing by the next highest number until you cannot divide anymore.

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

11729371934936291,0733,2815,5977,14118,24195,149121,397207,0893,520,513
-1-17-29-37-193-493-629-1,073-3,281-5,597-7,141-18,241-95,149-121,397-207,089-3,520,513

More Examples

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