Q: What are the factor combinations of the number 221,633,233?

 A:
Positive:   1 x 22163323317 x 1303724919 x 11664907181 x 1224493223 x 993871289 x 766897323 x 6861713077 x 720293439 x 644473791 x 584634237 x 523095491 x 40363
Negative: -1 x -221633233-17 x -13037249-19 x -11664907-181 x -1224493-223 x -993871-289 x -766897-323 x -686171-3077 x -72029-3439 x -64447-3791 x -58463-4237 x -52309-5491 x -40363


How do I find the factor combinations of the number 221,633,233?

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 221,633,233, 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.

1 221,633,233
-1 -221,633,233

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 221,633,233.

Example:
1 x 221,633,233 = 221,633,233
and
-1 x -221,633,233 = 221,633,233
Notice both answers equal 221,633,233

With that explanation out of the way, let's continue. Next, we take the number 221,633,233 and divide it by 2:

221,633,233 ÷ 2 = 110,816,616.5

If the quotient is a whole number, then 2 and 110,816,616.5 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:

1 221,633,233
-1 -221,633,233

Now, we try dividing 221,633,233 by 3:

221,633,233 ÷ 3 = 73,877,744.3333

If the quotient is a whole number, then 3 and 73,877,744.3333 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:

1 221,633,233
-1 -221,633,233

Let's try dividing by 4:

221,633,233 ÷ 4 = 55,408,308.25

If the quotient is a whole number, then 4 and 55,408,308.25 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:

1 221,633,233
-1 221,633,233
Keep dividing by the next highest number until you cannot divide anymore.

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

117191812232893233,0773,4393,7914,2375,49140,36352,30958,46364,44772,029686,171766,897993,8711,224,49311,664,90713,037,249221,633,233
-1-17-19-181-223-289-323-3,077-3,439-3,791-4,237-5,491-40,363-52,309-58,463-64,447-72,029-686,171-766,897-993,871-1,224,493-11,664,907-13,037,249-221,633,233

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