Q: What are the factor combinations of the number 40,688,081?

 A:
Positive:   1 x 406880817 x 581258323 x 176904749 x 83036979 x 515039161 x 252721457 x 89033553 x 735771127 x 361031817 x 223933199 x 127193871 x 10511
Negative: -1 x -40688081-7 x -5812583-23 x -1769047-49 x -830369-79 x -515039-161 x -252721-457 x -89033-553 x -73577-1127 x -36103-1817 x -22393-3199 x -12719-3871 x -10511


How do I find the factor combinations of the number 40,688,081?

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 40,688,081, 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 40,688,081
-1 -40,688,081

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 40,688,081.

Example:
1 x 40,688,081 = 40,688,081
and
-1 x -40,688,081 = 40,688,081
Notice both answers equal 40,688,081

With that explanation out of the way, let's continue. Next, we take the number 40,688,081 and divide it by 2:

40,688,081 ÷ 2 = 20,344,040.5

If the quotient is a whole number, then 2 and 20,344,040.5 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 40,688,081
-1 -40,688,081

Now, we try dividing 40,688,081 by 3:

40,688,081 ÷ 3 = 13,562,693.6667

If the quotient is a whole number, then 3 and 13,562,693.6667 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 40,688,081
-1 -40,688,081

Let's try dividing by 4:

40,688,081 ÷ 4 = 10,172,020.25

If the quotient is a whole number, then 4 and 10,172,020.25 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 40,688,081
-1 40,688,081
Keep dividing by the next highest number until you cannot divide anymore.

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

172349791614575531,1271,8173,1993,87110,51112,71922,39336,10373,57789,033252,721515,039830,3691,769,0475,812,58340,688,081
-1-7-23-49-79-161-457-553-1,127-1,817-3,199-3,871-10,511-12,719-22,393-36,103-73,577-89,033-252,721-515,039-830,369-1,769,047-5,812,583-40,688,081

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