Q: What are the factor combinations of the number 403,631?

 A:
Positive:   1 x 40363117 x 23743
Negative: -1 x -403631-17 x -23743


How do I find the factor combinations of the number 403,631?

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 403,631, 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.

1 403,631
-1 -403,631

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 403,631.

Example:
1 x 403,631 = 403,631
and
-1 x -403,631 = 403,631
Notice both answers equal 403,631

With that explanation out of the way, let's continue. Next, we take the number 403,631 and divide it by 2:

403,631 ÷ 2 = 201,815.5

If the quotient is a whole number, then 2 and 201,815.5 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:

1 403,631
-1 -403,631

Now, we try dividing 403,631 by 3:

403,631 ÷ 3 = 134,543.6667

If the quotient is a whole number, then 3 and 134,543.6667 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:

1 403,631
-1 -403,631

Let's try dividing by 4:

403,631 ÷ 4 = 100,907.75

If the quotient is a whole number, then 4 and 100,907.75 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:

1 403,631
-1 403,631
Keep dividing by the next highest number until you cannot divide anymore.

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

11723,743403,631
-1-17-23,743-403,631

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 403,631:


Ask a Question