Q: What are the factor combinations of the number 123,240,221?

 A:
Positive:   1 x 12324022113 x 948001731 x 3975491103 x 1196507403 x 3058071339 x 920392969 x 415093193 x 38597
Negative: -1 x -123240221-13 x -9480017-31 x -3975491-103 x -1196507-403 x -305807-1339 x -92039-2969 x -41509-3193 x -38597


How do I find the factor combinations of the number 123,240,221?

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 123,240,221, 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.

1 123,240,221
-1 -123,240,221

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 123,240,221.

Example:
1 x 123,240,221 = 123,240,221
and
-1 x -123,240,221 = 123,240,221
Notice both answers equal 123,240,221

With that explanation out of the way, let's continue. Next, we take the number 123,240,221 and divide it by 2:

123,240,221 ÷ 2 = 61,620,110.5

If the quotient is a whole number, then 2 and 61,620,110.5 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:

1 123,240,221
-1 -123,240,221

Now, we try dividing 123,240,221 by 3:

123,240,221 ÷ 3 = 41,080,073.6667

If the quotient is a whole number, then 3 and 41,080,073.6667 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:

1 123,240,221
-1 -123,240,221

Let's try dividing by 4:

123,240,221 ÷ 4 = 30,810,055.25

If the quotient is a whole number, then 4 and 30,810,055.25 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:

1 123,240,221
-1 123,240,221
Keep dividing by the next highest number until you cannot divide anymore.

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

113311034031,3392,9693,19338,59741,50992,039305,8071,196,5073,975,4919,480,017123,240,221
-1-13-31-103-403-1,339-2,969-3,193-38,597-41,509-92,039-305,807-1,196,507-3,975,491-9,480,017-123,240,221

More Examples

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