Q: What are the factor combinations of the number 1,352,221?

 A:
Positive:   1 x 135222113 x 10401741 x 3298143 x 3144759 x 22919533 x 2537559 x 2419767 x 1763
Negative: -1 x -1352221-13 x -104017-41 x -32981-43 x -31447-59 x -22919-533 x -2537-559 x -2419-767 x -1763


How do I find the factor combinations of the number 1,352,221?

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 1,352,221, 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 1,352,221
-1 -1,352,221

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 1,352,221.

Example:
1 x 1,352,221 = 1,352,221
and
-1 x -1,352,221 = 1,352,221
Notice both answers equal 1,352,221

With that explanation out of the way, let's continue. Next, we take the number 1,352,221 and divide it by 2:

1,352,221 ÷ 2 = 676,110.5

If the quotient is a whole number, then 2 and 676,110.5 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 1,352,221
-1 -1,352,221

Now, we try dividing 1,352,221 by 3:

1,352,221 ÷ 3 = 450,740.3333

If the quotient is a whole number, then 3 and 450,740.3333 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 1,352,221
-1 -1,352,221

Let's try dividing by 4:

1,352,221 ÷ 4 = 338,055.25

If the quotient is a whole number, then 4 and 338,055.25 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 1,352,221
-1 1,352,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1134143595335597671,7632,4192,53722,91931,44732,981104,0171,352,221
-1-13-41-43-59-533-559-767-1,763-2,419-2,537-22,919-31,447-32,981-104,017-1,352,221

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