Q: What are the factor combinations of the number 8,240,221?

 A:
Positive:   1 x 824022111 x 74911141 x 200981121 x 68101151 x 54571451 x 182711331 x 61911661 x 4961
Negative: -1 x -8240221-11 x -749111-41 x -200981-121 x -68101-151 x -54571-451 x -18271-1331 x -6191-1661 x -4961


How do I find the factor combinations of the number 8,240,221?

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 8,240,221, 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 8,240,221
-1 -8,240,221

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 8,240,221.

Example:
1 x 8,240,221 = 8,240,221
and
-1 x -8,240,221 = 8,240,221
Notice both answers equal 8,240,221

With that explanation out of the way, let's continue. Next, we take the number 8,240,221 and divide it by 2:

8,240,221 ÷ 2 = 4,120,110.5

If the quotient is a whole number, then 2 and 4,120,110.5 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 8,240,221
-1 -8,240,221

Now, we try dividing 8,240,221 by 3:

8,240,221 ÷ 3 = 2,746,740.3333

If the quotient is a whole number, then 3 and 2,746,740.3333 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 8,240,221
-1 -8,240,221

Let's try dividing by 4:

8,240,221 ÷ 4 = 2,060,055.25

If the quotient is a whole number, then 4 and 2,060,055.25 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 8,240,221
-1 8,240,221
Keep dividing by the next highest number until you cannot divide anymore.

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

111411211514511,3311,6614,9616,19118,27154,57168,101200,981749,1118,240,221
-1-11-41-121-151-451-1,331-1,661-4,961-6,191-18,271-54,571-68,101-200,981-749,111-8,240,221

More Examples

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