Q: What are the factor combinations of the number 40,406,705?

 A:
Positive:   1 x 404067055 x 808134117 x 237686561 x 66240585 x 475373305 x 1324811037 x 389655185 x 7793
Negative: -1 x -40406705-5 x -8081341-17 x -2376865-61 x -662405-85 x -475373-305 x -132481-1037 x -38965-5185 x -7793


How do I find the factor combinations of the number 40,406,705?

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 40,406,705, 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 40,406,705
-1 -40,406,705

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 40,406,705.

Example:
1 x 40,406,705 = 40,406,705
and
-1 x -40,406,705 = 40,406,705
Notice both answers equal 40,406,705

With that explanation out of the way, let's continue. Next, we take the number 40,406,705 and divide it by 2:

40,406,705 ÷ 2 = 20,203,352.5

If the quotient is a whole number, then 2 and 20,203,352.5 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 40,406,705
-1 -40,406,705

Now, we try dividing 40,406,705 by 3:

40,406,705 ÷ 3 = 13,468,901.6667

If the quotient is a whole number, then 3 and 13,468,901.6667 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 40,406,705
-1 -40,406,705

Let's try dividing by 4:

40,406,705 ÷ 4 = 10,101,676.25

If the quotient is a whole number, then 4 and 10,101,676.25 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 40,406,705
-1 40,406,705
Keep dividing by the next highest number until you cannot divide anymore.

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

151761853051,0375,1857,79338,965132,481475,373662,4052,376,8658,081,34140,406,705
-1-5-17-61-85-305-1,037-5,185-7,793-38,965-132,481-475,373-662,405-2,376,865-8,081,341-40,406,705

More Examples

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