Q: What are the factor combinations of the number 401,110,045?

 A:
Positive:   1 x 4011100455 x 802220097 x 5730143519 x 2111105535 x 1146028795 x 4222211133 x 3015865665 x 603173
Negative: -1 x -401110045-5 x -80222009-7 x -57301435-19 x -21111055-35 x -11460287-95 x -4222211-133 x -3015865-665 x -603173


How do I find the factor combinations of the number 401,110,045?

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 401,110,045, 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.

1 401,110,045
-1 -401,110,045

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 401,110,045.

Example:
1 x 401,110,045 = 401,110,045
and
-1 x -401,110,045 = 401,110,045
Notice both answers equal 401,110,045

With that explanation out of the way, let's continue. Next, we take the number 401,110,045 and divide it by 2:

401,110,045 ÷ 2 = 200,555,022.5

If the quotient is a whole number, then 2 and 200,555,022.5 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:

1 401,110,045
-1 -401,110,045

Now, we try dividing 401,110,045 by 3:

401,110,045 ÷ 3 = 133,703,348.3333

If the quotient is a whole number, then 3 and 133,703,348.3333 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:

1 401,110,045
-1 -401,110,045

Let's try dividing by 4:

401,110,045 ÷ 4 = 100,277,511.25

If the quotient is a whole number, then 4 and 100,277,511.25 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:

1 401,110,045
-1 401,110,045
Keep dividing by the next highest number until you cannot divide anymore.

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

157193595133665603,1733,015,8654,222,21111,460,28721,111,05557,301,43580,222,009401,110,045
-1-5-7-19-35-95-133-665-603,173-3,015,865-4,222,211-11,460,287-21,111,055-57,301,435-80,222,009-401,110,045

More Examples

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