Q: What are the factor combinations of the number 230,302,331?

 A:
Positive:   1 x 2303023317 x 3290033353 x 4345327151 x 1525181371 x 6207611057 x 2178834111 x 560218003 x 28777
Negative: -1 x -230302331-7 x -32900333-53 x -4345327-151 x -1525181-371 x -620761-1057 x -217883-4111 x -56021-8003 x -28777


How do I find the factor combinations of the number 230,302,331?

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 230,302,331, 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.

1 230,302,331
-1 -230,302,331

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 230,302,331.

Example:
1 x 230,302,331 = 230,302,331
and
-1 x -230,302,331 = 230,302,331
Notice both answers equal 230,302,331

With that explanation out of the way, let's continue. Next, we take the number 230,302,331 and divide it by 2:

230,302,331 ÷ 2 = 115,151,165.5

If the quotient is a whole number, then 2 and 115,151,165.5 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:

1 230,302,331
-1 -230,302,331

Now, we try dividing 230,302,331 by 3:

230,302,331 ÷ 3 = 76,767,443.6667

If the quotient is a whole number, then 3 and 76,767,443.6667 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:

1 230,302,331
-1 -230,302,331

Let's try dividing by 4:

230,302,331 ÷ 4 = 57,575,582.75

If the quotient is a whole number, then 4 and 57,575,582.75 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:

1 230,302,331
-1 230,302,331
Keep dividing by the next highest number until you cannot divide anymore.

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

17531513711,0574,1118,00328,77756,021217,883620,7611,525,1814,345,32732,900,333230,302,331
-1-7-53-151-371-1,057-4,111-8,003-28,777-56,021-217,883-620,761-1,525,181-4,345,327-32,900,333-230,302,331

More Examples

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