Q: What are the factor combinations of the number 230,240,309?

 A:
Positive:   1 x 23024030913 x 1771079319 x 1211791129 x 7939321247 x 932147377 x 610717551 x 4178597163 x 32143
Negative: -1 x -230240309-13 x -17710793-19 x -12117911-29 x -7939321-247 x -932147-377 x -610717-551 x -417859-7163 x -32143


How do I find the factor combinations of the number 230,240,309?

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 230,240,309, 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.

1 230,240,309
-1 -230,240,309

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 230,240,309.

Example:
1 x 230,240,309 = 230,240,309
and
-1 x -230,240,309 = 230,240,309
Notice both answers equal 230,240,309

With that explanation out of the way, let's continue. Next, we take the number 230,240,309 and divide it by 2:

230,240,309 ÷ 2 = 115,120,154.5

If the quotient is a whole number, then 2 and 115,120,154.5 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:

1 230,240,309
-1 -230,240,309

Now, we try dividing 230,240,309 by 3:

230,240,309 ÷ 3 = 76,746,769.6667

If the quotient is a whole number, then 3 and 76,746,769.6667 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:

1 230,240,309
-1 -230,240,309

Let's try dividing by 4:

230,240,309 ÷ 4 = 57,560,077.25

If the quotient is a whole number, then 4 and 57,560,077.25 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:

1 230,240,309
-1 230,240,309
Keep dividing by the next highest number until you cannot divide anymore.

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

11319292473775517,16332,143417,859610,717932,1477,939,32112,117,91117,710,793230,240,309
-1-13-19-29-247-377-551-7,163-32,143-417,859-610,717-932,147-7,939,321-12,117,911-17,710,793-230,240,309

More Examples

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