Q: What are the factor combinations of the number 40,322,125?

 A:
Positive:   1 x 403221255 x 806442525 x 1612885125 x 322577163 x 247375815 x 494751979 x 203754075 x 9895
Negative: -1 x -40322125-5 x -8064425-25 x -1612885-125 x -322577-163 x -247375-815 x -49475-1979 x -20375-4075 x -9895


How do I find the factor combinations of the number 40,322,125?

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 40,322,125, 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 40,322,125
-1 -40,322,125

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 40,322,125.

Example:
1 x 40,322,125 = 40,322,125
and
-1 x -40,322,125 = 40,322,125
Notice both answers equal 40,322,125

With that explanation out of the way, let's continue. Next, we take the number 40,322,125 and divide it by 2:

40,322,125 ÷ 2 = 20,161,062.5

If the quotient is a whole number, then 2 and 20,161,062.5 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 40,322,125
-1 -40,322,125

Now, we try dividing 40,322,125 by 3:

40,322,125 ÷ 3 = 13,440,708.3333

If the quotient is a whole number, then 3 and 13,440,708.3333 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 40,322,125
-1 -40,322,125

Let's try dividing by 4:

40,322,125 ÷ 4 = 10,080,531.25

If the quotient is a whole number, then 4 and 10,080,531.25 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 40,322,125
-1 40,322,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251251638151,9794,0759,89520,37549,475247,375322,5771,612,8858,064,42540,322,125
-1-5-25-125-163-815-1,979-4,075-9,895-20,375-49,475-247,375-322,577-1,612,885-8,064,425-40,322,125

More Examples

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