Q: What are the factor combinations of the number 210,312,235?

 A:
Positive:   1 x 2103122355 x 420624477 x 3004460519 x 1106906535 x 600892195 x 2213813133 x 1581295665 x 316259
Negative: -1 x -210312235-5 x -42062447-7 x -30044605-19 x -11069065-35 x -6008921-95 x -2213813-133 x -1581295-665 x -316259


How do I find the factor combinations of the number 210,312,235?

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 210,312,235, 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.

1 210,312,235
-1 -210,312,235

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 210,312,235.

Example:
1 x 210,312,235 = 210,312,235
and
-1 x -210,312,235 = 210,312,235
Notice both answers equal 210,312,235

With that explanation out of the way, let's continue. Next, we take the number 210,312,235 and divide it by 2:

210,312,235 ÷ 2 = 105,156,117.5

If the quotient is a whole number, then 2 and 105,156,117.5 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:

1 210,312,235
-1 -210,312,235

Now, we try dividing 210,312,235 by 3:

210,312,235 ÷ 3 = 70,104,078.3333

If the quotient is a whole number, then 3 and 70,104,078.3333 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:

1 210,312,235
-1 -210,312,235

Let's try dividing by 4:

210,312,235 ÷ 4 = 52,578,058.75

If the quotient is a whole number, then 4 and 52,578,058.75 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:

1 210,312,235
-1 210,312,235
Keep dividing by the next highest number until you cannot divide anymore.

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

157193595133665316,2591,581,2952,213,8136,008,92111,069,06530,044,60542,062,447210,312,235
-1-5-7-19-35-95-133-665-316,259-1,581,295-2,213,813-6,008,921-11,069,065-30,044,605-42,062,447-210,312,235

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