Q: What are the factor combinations of the number 3,520,517?

 A:
Positive:   1 x 35205177 x 50293111 x 32004713 x 27080977 x 4572191 x 38687143 x 246191001 x 3517
Negative: -1 x -3520517-7 x -502931-11 x -320047-13 x -270809-77 x -45721-91 x -38687-143 x -24619-1001 x -3517


How do I find the factor combinations of the number 3,520,517?

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 3,520,517, 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 3,520,517
-1 -3,520,517

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 3,520,517.

Example:
1 x 3,520,517 = 3,520,517
and
-1 x -3,520,517 = 3,520,517
Notice both answers equal 3,520,517

With that explanation out of the way, let's continue. Next, we take the number 3,520,517 and divide it by 2:

3,520,517 ÷ 2 = 1,760,258.5

If the quotient is a whole number, then 2 and 1,760,258.5 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 3,520,517
-1 -3,520,517

Now, we try dividing 3,520,517 by 3:

3,520,517 ÷ 3 = 1,173,505.6667

If the quotient is a whole number, then 3 and 1,173,505.6667 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 3,520,517
-1 -3,520,517

Let's try dividing by 4:

3,520,517 ÷ 4 = 880,129.25

If the quotient is a whole number, then 4 and 880,129.25 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 3,520,517
-1 3,520,517
Keep dividing by the next highest number until you cannot divide anymore.

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

17111377911431,0013,51724,61938,68745,721270,809320,047502,9313,520,517
-1-7-11-13-77-91-143-1,001-3,517-24,619-38,687-45,721-270,809-320,047-502,931-3,520,517

More Examples

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