Q: What are the factor combinations of the number 426,476?

 A:
Positive:   1 x 4264762 x 2132384 x 106619
Negative: -1 x -426476-2 x -213238-4 x -106619


How do I find the factor combinations of the number 426,476?

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 426,476, 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.

1 426,476
-1 -426,476

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 426,476.

Example:
1 x 426,476 = 426,476
and
-1 x -426,476 = 426,476
Notice both answers equal 426,476

With that explanation out of the way, let's continue. Next, we take the number 426,476 and divide it by 2:

426,476 ÷ 2 = 213,238

If the quotient is a whole number, then 2 and 213,238 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 213,238 426,476
-1 -2 -213,238 -426,476

Now, we try dividing 426,476 by 3:

426,476 ÷ 3 = 142,158.6667

If the quotient is a whole number, then 3 and 142,158.6667 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 2 213,238 426,476
-1 -2 -213,238 -426,476

Let's try dividing by 4:

426,476 ÷ 4 = 106,619

If the quotient is a whole number, then 4 and 106,619 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 106,619 213,238 426,476
-1 -2 -4 -106,619 -213,238 426,476
Keep dividing by the next highest number until you cannot divide anymore.

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

124106,619213,238426,476
-1-2-4-106,619-213,238-426,476

More Examples

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