Q: What are the factor combinations of the number 346,389?

 A:
Positive:   1 x 3463893 x 11546319 x 1823157 x 607759 x 5871103 x 3363177 x 1957309 x 1121
Negative: -1 x -346389-3 x -115463-19 x -18231-57 x -6077-59 x -5871-103 x -3363-177 x -1957-309 x -1121


How do I find the factor combinations of the number 346,389?

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 346,389, 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.

1 346,389
-1 -346,389

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 346,389.

Example:
1 x 346,389 = 346,389
and
-1 x -346,389 = 346,389
Notice both answers equal 346,389

With that explanation out of the way, let's continue. Next, we take the number 346,389 and divide it by 2:

346,389 ÷ 2 = 173,194.5

If the quotient is a whole number, then 2 and 173,194.5 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:

1 346,389
-1 -346,389

Now, we try dividing 346,389 by 3:

346,389 ÷ 3 = 115,463

If the quotient is a whole number, then 3 and 115,463 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 3 115,463 346,389
-1 -3 -115,463 -346,389

Let's try dividing by 4:

346,389 ÷ 4 = 86,597.25

If the quotient is a whole number, then 4 and 86,597.25 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 3 115,463 346,389
-1 -3 -115,463 346,389
Keep dividing by the next highest number until you cannot divide anymore.

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

131957591031773091,1211,9573,3635,8716,07718,231115,463346,389
-1-3-19-57-59-103-177-309-1,121-1,957-3,363-5,871-6,077-18,231-115,463-346,389

More Examples

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