Q: What are the factor combinations of the number 40,638,715?

 A:
Positive:   1 x 406387155 x 812774313 x 312605529 x 140133565 x 625211145 x 280267377 x 1077951885 x 21559
Negative: -1 x -40638715-5 x -8127743-13 x -3126055-29 x -1401335-65 x -625211-145 x -280267-377 x -107795-1885 x -21559


How do I find the factor combinations of the number 40,638,715?

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 40,638,715, 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 40,638,715
-1 -40,638,715

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 40,638,715.

Example:
1 x 40,638,715 = 40,638,715
and
-1 x -40,638,715 = 40,638,715
Notice both answers equal 40,638,715

With that explanation out of the way, let's continue. Next, we take the number 40,638,715 and divide it by 2:

40,638,715 ÷ 2 = 20,319,357.5

If the quotient is a whole number, then 2 and 20,319,357.5 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 40,638,715
-1 -40,638,715

Now, we try dividing 40,638,715 by 3:

40,638,715 ÷ 3 = 13,546,238.3333

If the quotient is a whole number, then 3 and 13,546,238.3333 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 40,638,715
-1 -40,638,715

Let's try dividing by 4:

40,638,715 ÷ 4 = 10,159,678.75

If the quotient is a whole number, then 4 and 10,159,678.75 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 40,638,715
-1 40,638,715
Keep dividing by the next highest number until you cannot divide anymore.

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

151329651453771,88521,559107,795280,267625,2111,401,3353,126,0558,127,74340,638,715
-1-5-13-29-65-145-377-1,885-21,559-107,795-280,267-625,211-1,401,335-3,126,055-8,127,743-40,638,715

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