Q: What are the factor combinations of the number 40,221,905?

 A:
Positive:   1 x 402219055 x 804438173 x 550985263 x 152935365 x 110197419 x 959951315 x 305872095 x 19199
Negative: -1 x -40221905-5 x -8044381-73 x -550985-263 x -152935-365 x -110197-419 x -95995-1315 x -30587-2095 x -19199


How do I find the factor combinations of the number 40,221,905?

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 40,221,905, 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 40,221,905
-1 -40,221,905

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 40,221,905.

Example:
1 x 40,221,905 = 40,221,905
and
-1 x -40,221,905 = 40,221,905
Notice both answers equal 40,221,905

With that explanation out of the way, let's continue. Next, we take the number 40,221,905 and divide it by 2:

40,221,905 ÷ 2 = 20,110,952.5

If the quotient is a whole number, then 2 and 20,110,952.5 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 40,221,905
-1 -40,221,905

Now, we try dividing 40,221,905 by 3:

40,221,905 ÷ 3 = 13,407,301.6667

If the quotient is a whole number, then 3 and 13,407,301.6667 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 40,221,905
-1 -40,221,905

Let's try dividing by 4:

40,221,905 ÷ 4 = 10,055,476.25

If the quotient is a whole number, then 4 and 10,055,476.25 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 40,221,905
-1 40,221,905
Keep dividing by the next highest number until you cannot divide anymore.

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

15732633654191,3152,09519,19930,58795,995110,197152,935550,9858,044,38140,221,905
-1-5-73-263-365-419-1,315-2,095-19,199-30,587-95,995-110,197-152,935-550,985-8,044,381-40,221,905

More Examples

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