Q: What are the factor combinations of the number 221,324,005?

 A:
Positive:   1 x 2213240055 x 442648017 x 3161771535 x 6323543839 x 2637954195 x 527595873 x 376857537 x 29365
Negative: -1 x -221324005-5 x -44264801-7 x -31617715-35 x -6323543-839 x -263795-4195 x -52759-5873 x -37685-7537 x -29365


How do I find the factor combinations of the number 221,324,005?

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 221,324,005, 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.

1 221,324,005
-1 -221,324,005

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 221,324,005.

Example:
1 x 221,324,005 = 221,324,005
and
-1 x -221,324,005 = 221,324,005
Notice both answers equal 221,324,005

With that explanation out of the way, let's continue. Next, we take the number 221,324,005 and divide it by 2:

221,324,005 ÷ 2 = 110,662,002.5

If the quotient is a whole number, then 2 and 110,662,002.5 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:

1 221,324,005
-1 -221,324,005

Now, we try dividing 221,324,005 by 3:

221,324,005 ÷ 3 = 73,774,668.3333

If the quotient is a whole number, then 3 and 73,774,668.3333 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:

1 221,324,005
-1 -221,324,005

Let's try dividing by 4:

221,324,005 ÷ 4 = 55,331,001.25

If the quotient is a whole number, then 4 and 55,331,001.25 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:

1 221,324,005
-1 221,324,005
Keep dividing by the next highest number until you cannot divide anymore.

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

157358394,1955,8737,53729,36537,68552,759263,7956,323,54331,617,71544,264,801221,324,005
-1-5-7-35-839-4,195-5,873-7,537-29,365-37,685-52,759-263,795-6,323,543-31,617,715-44,264,801-221,324,005

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