Q: What are the factor combinations of the number 104,411,321?

 A:
Positive:   1 x 1044113217 x 1491590361 x 1711661427 x 244523439 x 237839557 x 1874533073 x 339773899 x 26779
Negative: -1 x -104411321-7 x -14915903-61 x -1711661-427 x -244523-439 x -237839-557 x -187453-3073 x -33977-3899 x -26779


How do I find the factor combinations of the number 104,411,321?

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 104,411,321, 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.

1 104,411,321
-1 -104,411,321

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 104,411,321.

Example:
1 x 104,411,321 = 104,411,321
and
-1 x -104,411,321 = 104,411,321
Notice both answers equal 104,411,321

With that explanation out of the way, let's continue. Next, we take the number 104,411,321 and divide it by 2:

104,411,321 ÷ 2 = 52,205,660.5

If the quotient is a whole number, then 2 and 52,205,660.5 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:

1 104,411,321
-1 -104,411,321

Now, we try dividing 104,411,321 by 3:

104,411,321 ÷ 3 = 34,803,773.6667

If the quotient is a whole number, then 3 and 34,803,773.6667 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:

1 104,411,321
-1 -104,411,321

Let's try dividing by 4:

104,411,321 ÷ 4 = 26,102,830.25

If the quotient is a whole number, then 4 and 26,102,830.25 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:

1 104,411,321
-1 104,411,321
Keep dividing by the next highest number until you cannot divide anymore.

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

17614274395573,0733,89926,77933,977187,453237,839244,5231,711,66114,915,903104,411,321
-1-7-61-427-439-557-3,073-3,899-26,779-33,977-187,453-237,839-244,523-1,711,661-14,915,903-104,411,321

More Examples

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