Q: What are the factor combinations of the number 345,016,321?

 A:
Positive:   1 x 34501632113 x 26539717
Negative: -1 x -345016321-13 x -26539717


How do I find the factor combinations of the number 345,016,321?

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 345,016,321, 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.

1 345,016,321
-1 -345,016,321

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 345,016,321.

Example:
1 x 345,016,321 = 345,016,321
and
-1 x -345,016,321 = 345,016,321
Notice both answers equal 345,016,321

With that explanation out of the way, let's continue. Next, we take the number 345,016,321 and divide it by 2:

345,016,321 ÷ 2 = 172,508,160.5

If the quotient is a whole number, then 2 and 172,508,160.5 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:

1 345,016,321
-1 -345,016,321

Now, we try dividing 345,016,321 by 3:

345,016,321 ÷ 3 = 115,005,440.3333

If the quotient is a whole number, then 3 and 115,005,440.3333 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:

1 345,016,321
-1 -345,016,321

Let's try dividing by 4:

345,016,321 ÷ 4 = 86,254,080.25

If the quotient is a whole number, then 4 and 86,254,080.25 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:

1 345,016,321
-1 345,016,321
Keep dividing by the next highest number until you cannot divide anymore.

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

11326,539,717345,016,321
-1-13-26,539,717-345,016,321

More Examples

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