Q: What are the factor combinations of the number 104,404,405?

 A:
Positive:   1 x 1044044055 x 208808817 x 1491491535 x 2982983103 x 1013635515 x 202727721 x 1448053605 x 28961
Negative: -1 x -104404405-5 x -20880881-7 x -14914915-35 x -2982983-103 x -1013635-515 x -202727-721 x -144805-3605 x -28961


How do I find the factor combinations of the number 104,404,405?

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 104,404,405, 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.

1 104,404,405
-1 -104,404,405

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 104,404,405.

Example:
1 x 104,404,405 = 104,404,405
and
-1 x -104,404,405 = 104,404,405
Notice both answers equal 104,404,405

With that explanation out of the way, let's continue. Next, we take the number 104,404,405 and divide it by 2:

104,404,405 ÷ 2 = 52,202,202.5

If the quotient is a whole number, then 2 and 52,202,202.5 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:

1 104,404,405
-1 -104,404,405

Now, we try dividing 104,404,405 by 3:

104,404,405 ÷ 3 = 34,801,468.3333

If the quotient is a whole number, then 3 and 34,801,468.3333 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:

1 104,404,405
-1 -104,404,405

Let's try dividing by 4:

104,404,405 ÷ 4 = 26,101,101.25

If the quotient is a whole number, then 4 and 26,101,101.25 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:

1 104,404,405
-1 104,404,405
Keep dividing by the next highest number until you cannot divide anymore.

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

157351035157213,60528,961144,805202,7271,013,6352,982,98314,914,91520,880,881104,404,405
-1-5-7-35-103-515-721-3,605-28,961-144,805-202,727-1,013,635-2,982,983-14,914,915-20,880,881-104,404,405

More Examples

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