Q: What are the factor combinations of the number 221,212,345?

 A:
Positive:   1 x 2212123455 x 4424246919 x 1164275595 x 2328551421 x 5254452105 x 1050895531 x 399957999 x 27655
Negative: -1 x -221212345-5 x -44242469-19 x -11642755-95 x -2328551-421 x -525445-2105 x -105089-5531 x -39995-7999 x -27655


How do I find the factor combinations of the number 221,212,345?

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 221,212,345, 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.

1 221,212,345
-1 -221,212,345

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 221,212,345.

Example:
1 x 221,212,345 = 221,212,345
and
-1 x -221,212,345 = 221,212,345
Notice both answers equal 221,212,345

With that explanation out of the way, let's continue. Next, we take the number 221,212,345 and divide it by 2:

221,212,345 ÷ 2 = 110,606,172.5

If the quotient is a whole number, then 2 and 110,606,172.5 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:

1 221,212,345
-1 -221,212,345

Now, we try dividing 221,212,345 by 3:

221,212,345 ÷ 3 = 73,737,448.3333

If the quotient is a whole number, then 3 and 73,737,448.3333 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:

1 221,212,345
-1 -221,212,345

Let's try dividing by 4:

221,212,345 ÷ 4 = 55,303,086.25

If the quotient is a whole number, then 4 and 55,303,086.25 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:

1 221,212,345
-1 221,212,345
Keep dividing by the next highest number until you cannot divide anymore.

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

1519954212,1055,5317,99927,65539,995105,089525,4452,328,55111,642,75544,242,469221,212,345
-1-5-19-95-421-2,105-5,531-7,999-27,655-39,995-105,089-525,445-2,328,551-11,642,755-44,242,469-221,212,345

More Examples

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