Q: What are the factor combinations of the number 310,233,235?

 A:
Positive:   1 x 3102332355 x 6204664713 x 2386409519 x 1632806565 x 477281995 x 3265613247 x 12560051235 x 251201
Negative: -1 x -310233235-5 x -62046647-13 x -23864095-19 x -16328065-65 x -4772819-95 x -3265613-247 x -1256005-1235 x -251201


How do I find the factor combinations of the number 310,233,235?

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 310,233,235, 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.

1 310,233,235
-1 -310,233,235

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 310,233,235.

Example:
1 x 310,233,235 = 310,233,235
and
-1 x -310,233,235 = 310,233,235
Notice both answers equal 310,233,235

With that explanation out of the way, let's continue. Next, we take the number 310,233,235 and divide it by 2:

310,233,235 ÷ 2 = 155,116,617.5

If the quotient is a whole number, then 2 and 155,116,617.5 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:

1 310,233,235
-1 -310,233,235

Now, we try dividing 310,233,235 by 3:

310,233,235 ÷ 3 = 103,411,078.3333

If the quotient is a whole number, then 3 and 103,411,078.3333 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:

1 310,233,235
-1 -310,233,235

Let's try dividing by 4:

310,233,235 ÷ 4 = 77,558,308.75

If the quotient is a whole number, then 4 and 77,558,308.75 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:

1 310,233,235
-1 310,233,235
Keep dividing by the next highest number until you cannot divide anymore.

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

15131965952471,235251,2011,256,0053,265,6134,772,81916,328,06523,864,09562,046,647310,233,235
-1-5-13-19-65-95-247-1,235-251,201-1,256,005-3,265,613-4,772,819-16,328,065-23,864,095-62,046,647-310,233,235

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