Q: What are the factor combinations of the number 3,407,815?

 A:
Positive:   1 x 34078155 x 681563
Negative: -1 x -3407815-5 x -681563


How do I find the factor combinations of the number 3,407,815?

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 3,407,815, 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 3,407,815
-1 -3,407,815

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 3,407,815.

Example:
1 x 3,407,815 = 3,407,815
and
-1 x -3,407,815 = 3,407,815
Notice both answers equal 3,407,815

With that explanation out of the way, let's continue. Next, we take the number 3,407,815 and divide it by 2:

3,407,815 ÷ 2 = 1,703,907.5

If the quotient is a whole number, then 2 and 1,703,907.5 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 3,407,815
-1 -3,407,815

Now, we try dividing 3,407,815 by 3:

3,407,815 ÷ 3 = 1,135,938.3333

If the quotient is a whole number, then 3 and 1,135,938.3333 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 3,407,815
-1 -3,407,815

Let's try dividing by 4:

3,407,815 ÷ 4 = 851,953.75

If the quotient is a whole number, then 4 and 851,953.75 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 3,407,815
-1 3,407,815
Keep dividing by the next highest number until you cannot divide anymore.

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

15681,5633,407,815
-1-5-681,563-3,407,815

More Examples

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