Q: What are the factor combinations of the number 673,589?

 A:
Positive:   1 x 6735897 x 9622741 x 16429287 x 2347
Negative: -1 x -673589-7 x -96227-41 x -16429-287 x -2347


How do I find the factor combinations of the number 673,589?

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 673,589, 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.

1 673,589
-1 -673,589

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 673,589.

Example:
1 x 673,589 = 673,589
and
-1 x -673,589 = 673,589
Notice both answers equal 673,589

With that explanation out of the way, let's continue. Next, we take the number 673,589 and divide it by 2:

673,589 ÷ 2 = 336,794.5

If the quotient is a whole number, then 2 and 336,794.5 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:

1 673,589
-1 -673,589

Now, we try dividing 673,589 by 3:

673,589 ÷ 3 = 224,529.6667

If the quotient is a whole number, then 3 and 224,529.6667 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:

1 673,589
-1 -673,589

Let's try dividing by 4:

673,589 ÷ 4 = 168,397.25

If the quotient is a whole number, then 4 and 168,397.25 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:

1 673,589
-1 673,589
Keep dividing by the next highest number until you cannot divide anymore.

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

17412872,34716,42996,227673,589
-1-7-41-287-2,347-16,429-96,227-673,589

More Examples

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