Q: What are the factor combinations of the number 40,404,221?

 A:
Positive:   1 x 4040422111 x 367311113 x 310801729 x 1393249143 x 282547319 x 126659377 x 1071734147 x 9743
Negative: -1 x -40404221-11 x -3673111-13 x -3108017-29 x -1393249-143 x -282547-319 x -126659-377 x -107173-4147 x -9743


How do I find the factor combinations of the number 40,404,221?

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 40,404,221, 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 40,404,221
-1 -40,404,221

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 40,404,221.

Example:
1 x 40,404,221 = 40,404,221
and
-1 x -40,404,221 = 40,404,221
Notice both answers equal 40,404,221

With that explanation out of the way, let's continue. Next, we take the number 40,404,221 and divide it by 2:

40,404,221 ÷ 2 = 20,202,110.5

If the quotient is a whole number, then 2 and 20,202,110.5 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 40,404,221
-1 -40,404,221

Now, we try dividing 40,404,221 by 3:

40,404,221 ÷ 3 = 13,468,073.6667

If the quotient is a whole number, then 3 and 13,468,073.6667 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 40,404,221
-1 -40,404,221

Let's try dividing by 4:

40,404,221 ÷ 4 = 10,101,055.25

If the quotient is a whole number, then 4 and 10,101,055.25 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 40,404,221
-1 40,404,221
Keep dividing by the next highest number until you cannot divide anymore.

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

11113291433193774,1479,743107,173126,659282,5471,393,2493,108,0173,673,11140,404,221
-1-11-13-29-143-319-377-4,147-9,743-107,173-126,659-282,547-1,393,249-3,108,017-3,673,111-40,404,221

More Examples

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