Q: What are the factor combinations of the number 346,291?

 A:
Positive:   1 x 34629111 x 31481
Negative: -1 x -346291-11 x -31481


How do I find the factor combinations of the number 346,291?

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 346,291, 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.

1 346,291
-1 -346,291

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 346,291.

Example:
1 x 346,291 = 346,291
and
-1 x -346,291 = 346,291
Notice both answers equal 346,291

With that explanation out of the way, let's continue. Next, we take the number 346,291 and divide it by 2:

346,291 ÷ 2 = 173,145.5

If the quotient is a whole number, then 2 and 173,145.5 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:

1 346,291
-1 -346,291

Now, we try dividing 346,291 by 3:

346,291 ÷ 3 = 115,430.3333

If the quotient is a whole number, then 3 and 115,430.3333 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:

1 346,291
-1 -346,291

Let's try dividing by 4:

346,291 ÷ 4 = 86,572.75

If the quotient is a whole number, then 4 and 86,572.75 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:

1 346,291
-1 346,291
Keep dividing by the next highest number until you cannot divide anymore.

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

11131,481346,291
-1-11-31,481-346,291

More Examples

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