Q: What are the factor combinations of the number 220,021,105?

 A:
Positive:   1 x 2200211055 x 4400422123 x 956613531 x 7097455115 x 1913227155 x 1419491713 x 3085853565 x 61717
Negative: -1 x -220021105-5 x -44004221-23 x -9566135-31 x -7097455-115 x -1913227-155 x -1419491-713 x -308585-3565 x -61717


How do I find the factor combinations of the number 220,021,105?

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 220,021,105, 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.

1 220,021,105
-1 -220,021,105

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 220,021,105.

Example:
1 x 220,021,105 = 220,021,105
and
-1 x -220,021,105 = 220,021,105
Notice both answers equal 220,021,105

With that explanation out of the way, let's continue. Next, we take the number 220,021,105 and divide it by 2:

220,021,105 ÷ 2 = 110,010,552.5

If the quotient is a whole number, then 2 and 110,010,552.5 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:

1 220,021,105
-1 -220,021,105

Now, we try dividing 220,021,105 by 3:

220,021,105 ÷ 3 = 73,340,368.3333

If the quotient is a whole number, then 3 and 73,340,368.3333 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:

1 220,021,105
-1 -220,021,105

Let's try dividing by 4:

220,021,105 ÷ 4 = 55,005,276.25

If the quotient is a whole number, then 4 and 55,005,276.25 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:

1 220,021,105
-1 220,021,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1523311151557133,56561,717308,5851,419,4911,913,2277,097,4559,566,13544,004,221220,021,105
-1-5-23-31-115-155-713-3,565-61,717-308,585-1,419,491-1,913,227-7,097,455-9,566,135-44,004,221-220,021,105

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