Q: What are the factor combinations of the number 1,040,221?

 A:
Positive:   1 x 10402217 x 14860313 x 8001723 x 4522749 x 2122971 x 1465191 x 11431161 x 6461299 x 3479497 x 2093637 x 1633923 x 1127
Negative: -1 x -1040221-7 x -148603-13 x -80017-23 x -45227-49 x -21229-71 x -14651-91 x -11431-161 x -6461-299 x -3479-497 x -2093-637 x -1633-923 x -1127


How do I find the factor combinations of the number 1,040,221?

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 1,040,221, 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 1,040,221
-1 -1,040,221

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 1,040,221.

Example:
1 x 1,040,221 = 1,040,221
and
-1 x -1,040,221 = 1,040,221
Notice both answers equal 1,040,221

With that explanation out of the way, let's continue. Next, we take the number 1,040,221 and divide it by 2:

1,040,221 ÷ 2 = 520,110.5

If the quotient is a whole number, then 2 and 520,110.5 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 1,040,221
-1 -1,040,221

Now, we try dividing 1,040,221 by 3:

1,040,221 ÷ 3 = 346,740.3333

If the quotient is a whole number, then 3 and 346,740.3333 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 1,040,221
-1 -1,040,221

Let's try dividing by 4:

1,040,221 ÷ 4 = 260,055.25

If the quotient is a whole number, then 4 and 260,055.25 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 1,040,221
-1 1,040,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1713234971911612994976379231,1271,6332,0933,4796,46111,43114,65121,22945,22780,017148,6031,040,221
-1-7-13-23-49-71-91-161-299-497-637-923-1,127-1,633-2,093-3,479-6,461-11,431-14,651-21,229-45,227-80,017-148,603-1,040,221

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