Q: What are the factor combinations of the number 410,404,315?

 A:
Positive:   1 x 4104043155 x 820808634339 x 9458518917 x 21695
Negative: -1 x -410404315-5 x -82080863-4339 x -94585-18917 x -21695


How do I find the factor combinations of the number 410,404,315?

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 410,404,315, 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.

1 410,404,315
-1 -410,404,315

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 410,404,315.

Example:
1 x 410,404,315 = 410,404,315
and
-1 x -410,404,315 = 410,404,315
Notice both answers equal 410,404,315

With that explanation out of the way, let's continue. Next, we take the number 410,404,315 and divide it by 2:

410,404,315 ÷ 2 = 205,202,157.5

If the quotient is a whole number, then 2 and 205,202,157.5 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:

1 410,404,315
-1 -410,404,315

Now, we try dividing 410,404,315 by 3:

410,404,315 ÷ 3 = 136,801,438.3333

If the quotient is a whole number, then 3 and 136,801,438.3333 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:

1 410,404,315
-1 -410,404,315

Let's try dividing by 4:

410,404,315 ÷ 4 = 102,601,078.75

If the quotient is a whole number, then 4 and 102,601,078.75 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:

1 410,404,315
-1 410,404,315
Keep dividing by the next highest number until you cannot divide anymore.

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

154,33918,91721,69594,58582,080,863410,404,315
-1-5-4,339-18,917-21,695-94,585-82,080,863-410,404,315

More Examples

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