Q: What are the factor combinations of the number 217,656,963?

 A:
Positive:   1 x 2176569633 x 725523219 x 2418410727 x 806136981 x 2687123
Negative: -1 x -217656963-3 x -72552321-9 x -24184107-27 x -8061369-81 x -2687123


How do I find the factor combinations of the number 217,656,963?

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 217,656,963, 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.

1 217,656,963
-1 -217,656,963

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 217,656,963.

Example:
1 x 217,656,963 = 217,656,963
and
-1 x -217,656,963 = 217,656,963
Notice both answers equal 217,656,963

With that explanation out of the way, let's continue. Next, we take the number 217,656,963 and divide it by 2:

217,656,963 ÷ 2 = 108,828,481.5

If the quotient is a whole number, then 2 and 108,828,481.5 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:

1 217,656,963
-1 -217,656,963

Now, we try dividing 217,656,963 by 3:

217,656,963 ÷ 3 = 72,552,321

If the quotient is a whole number, then 3 and 72,552,321 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 72,552,321 217,656,963
-1 -3 -72,552,321 -217,656,963

Let's try dividing by 4:

217,656,963 ÷ 4 = 54,414,240.75

If the quotient is a whole number, then 4 and 54,414,240.75 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 3 72,552,321 217,656,963
-1 -3 -72,552,321 217,656,963
Keep dividing by the next highest number until you cannot divide anymore.

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

13927812,687,1238,061,36924,184,10772,552,321217,656,963
-1-3-9-27-81-2,687,123-8,061,369-24,184,107-72,552,321-217,656,963

More Examples

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