Q: What are the factor combinations of the number 304,112,003?

 A:
Positive:   1 x 30411200313 x 2339323123 x 13222261299 x 1017097
Negative: -1 x -304112003-13 x -23393231-23 x -13222261-299 x -1017097


How do I find the factor combinations of the number 304,112,003?

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 304,112,003, 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.

1 304,112,003
-1 -304,112,003

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 304,112,003.

Example:
1 x 304,112,003 = 304,112,003
and
-1 x -304,112,003 = 304,112,003
Notice both answers equal 304,112,003

With that explanation out of the way, let's continue. Next, we take the number 304,112,003 and divide it by 2:

304,112,003 ÷ 2 = 152,056,001.5

If the quotient is a whole number, then 2 and 152,056,001.5 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:

1 304,112,003
-1 -304,112,003

Now, we try dividing 304,112,003 by 3:

304,112,003 ÷ 3 = 101,370,667.6667

If the quotient is a whole number, then 3 and 101,370,667.6667 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:

1 304,112,003
-1 -304,112,003

Let's try dividing by 4:

304,112,003 ÷ 4 = 76,028,000.75

If the quotient is a whole number, then 4 and 76,028,000.75 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:

1 304,112,003
-1 304,112,003
Keep dividing by the next highest number until you cannot divide anymore.

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

113232991,017,09713,222,26123,393,231304,112,003
-1-13-23-299-1,017,097-13,222,261-23,393,231-304,112,003

More Examples

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