Q: What are the factor combinations of the number 423,479?

 A:
Positive:   1 x 4234797 x 60497
Negative: -1 x -423479-7 x -60497


How do I find the factor combinations of the number 423,479?

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 423,479, 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.

1 423,479
-1 -423,479

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 423,479.

Example:
1 x 423,479 = 423,479
and
-1 x -423,479 = 423,479
Notice both answers equal 423,479

With that explanation out of the way, let's continue. Next, we take the number 423,479 and divide it by 2:

423,479 ÷ 2 = 211,739.5

If the quotient is a whole number, then 2 and 211,739.5 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:

1 423,479
-1 -423,479

Now, we try dividing 423,479 by 3:

423,479 ÷ 3 = 141,159.6667

If the quotient is a whole number, then 3 and 141,159.6667 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:

1 423,479
-1 -423,479

Let's try dividing by 4:

423,479 ÷ 4 = 105,869.75

If the quotient is a whole number, then 4 and 105,869.75 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:

1 423,479
-1 423,479
Keep dividing by the next highest number until you cannot divide anymore.

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

1760,497423,479
-1-7-60,497-423,479

More Examples

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