Q: What are the factor combinations of the number 232,212,305?

 A:
Positive:   1 x 2322123055 x 4644246113 x 1786248565 x 3572497521 x 4457052605 x 891416773 x 342856857 x 33865
Negative: -1 x -232212305-5 x -46442461-13 x -17862485-65 x -3572497-521 x -445705-2605 x -89141-6773 x -34285-6857 x -33865


How do I find the factor combinations of the number 232,212,305?

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 232,212,305, 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.

1 232,212,305
-1 -232,212,305

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 232,212,305.

Example:
1 x 232,212,305 = 232,212,305
and
-1 x -232,212,305 = 232,212,305
Notice both answers equal 232,212,305

With that explanation out of the way, let's continue. Next, we take the number 232,212,305 and divide it by 2:

232,212,305 ÷ 2 = 116,106,152.5

If the quotient is a whole number, then 2 and 116,106,152.5 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:

1 232,212,305
-1 -232,212,305

Now, we try dividing 232,212,305 by 3:

232,212,305 ÷ 3 = 77,404,101.6667

If the quotient is a whole number, then 3 and 77,404,101.6667 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:

1 232,212,305
-1 -232,212,305

Let's try dividing by 4:

232,212,305 ÷ 4 = 58,053,076.25

If the quotient is a whole number, then 4 and 58,053,076.25 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:

1 232,212,305
-1 232,212,305
Keep dividing by the next highest number until you cannot divide anymore.

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

1513655212,6056,7736,85733,86534,28589,141445,7053,572,49717,862,48546,442,461232,212,305
-1-5-13-65-521-2,605-6,773-6,857-33,865-34,285-89,141-445,705-3,572,497-17,862,485-46,442,461-232,212,305

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