Q: What are the factor combinations of the number 313,404,049?

 A:
Positive:   1 x 3134040497 x 4477200723 x 1362626349 x 6396001161 x 19466091127 x 278087
Negative: -1 x -313404049-7 x -44772007-23 x -13626263-49 x -6396001-161 x -1946609-1127 x -278087


How do I find the factor combinations of the number 313,404,049?

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 313,404,049, 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.

1 313,404,049
-1 -313,404,049

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 313,404,049.

Example:
1 x 313,404,049 = 313,404,049
and
-1 x -313,404,049 = 313,404,049
Notice both answers equal 313,404,049

With that explanation out of the way, let's continue. Next, we take the number 313,404,049 and divide it by 2:

313,404,049 ÷ 2 = 156,702,024.5

If the quotient is a whole number, then 2 and 156,702,024.5 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:

1 313,404,049
-1 -313,404,049

Now, we try dividing 313,404,049 by 3:

313,404,049 ÷ 3 = 104,468,016.3333

If the quotient is a whole number, then 3 and 104,468,016.3333 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:

1 313,404,049
-1 -313,404,049

Let's try dividing by 4:

313,404,049 ÷ 4 = 78,351,012.25

If the quotient is a whole number, then 4 and 78,351,012.25 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:

1 313,404,049
-1 313,404,049
Keep dividing by the next highest number until you cannot divide anymore.

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

1723491611,127278,0871,946,6096,396,00113,626,26344,772,007313,404,049
-1-7-23-49-161-1,127-278,087-1,946,609-6,396,001-13,626,263-44,772,007-313,404,049

More Examples

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