Q: What are the factor combinations of the number 104,511,421?

 A:
Positive:   1 x 1045114217 x 1493020337 x 2824633259 x 403519271 x 3856511489 x 701891897 x 5509310027 x 10423
Negative: -1 x -104511421-7 x -14930203-37 x -2824633-259 x -403519-271 x -385651-1489 x -70189-1897 x -55093-10027 x -10423


How do I find the factor combinations of the number 104,511,421?

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 104,511,421, 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.

1 104,511,421
-1 -104,511,421

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 104,511,421.

Example:
1 x 104,511,421 = 104,511,421
and
-1 x -104,511,421 = 104,511,421
Notice both answers equal 104,511,421

With that explanation out of the way, let's continue. Next, we take the number 104,511,421 and divide it by 2:

104,511,421 ÷ 2 = 52,255,710.5

If the quotient is a whole number, then 2 and 52,255,710.5 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:

1 104,511,421
-1 -104,511,421

Now, we try dividing 104,511,421 by 3:

104,511,421 ÷ 3 = 34,837,140.3333

If the quotient is a whole number, then 3 and 34,837,140.3333 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:

1 104,511,421
-1 -104,511,421

Let's try dividing by 4:

104,511,421 ÷ 4 = 26,127,855.25

If the quotient is a whole number, then 4 and 26,127,855.25 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:

1 104,511,421
-1 104,511,421
Keep dividing by the next highest number until you cannot divide anymore.

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

17372592711,4891,89710,02710,42355,09370,189385,651403,5192,824,63314,930,203104,511,421
-1-7-37-259-271-1,489-1,897-10,027-10,423-55,093-70,189-385,651-403,519-2,824,633-14,930,203-104,511,421

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