Q: What are the factor combinations of the number 221,023,103?

 A:
Positive:   1 x 2210231037 x 3157472917 x 13001359119 x 1857337563 x 3925813299 x 669973941 x 560839571 x 23093
Negative: -1 x -221023103-7 x -31574729-17 x -13001359-119 x -1857337-563 x -392581-3299 x -66997-3941 x -56083-9571 x -23093


How do I find the factor combinations of the number 221,023,103?

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 221,023,103, 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.

1 221,023,103
-1 -221,023,103

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 221,023,103.

Example:
1 x 221,023,103 = 221,023,103
and
-1 x -221,023,103 = 221,023,103
Notice both answers equal 221,023,103

With that explanation out of the way, let's continue. Next, we take the number 221,023,103 and divide it by 2:

221,023,103 ÷ 2 = 110,511,551.5

If the quotient is a whole number, then 2 and 110,511,551.5 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:

1 221,023,103
-1 -221,023,103

Now, we try dividing 221,023,103 by 3:

221,023,103 ÷ 3 = 73,674,367.6667

If the quotient is a whole number, then 3 and 73,674,367.6667 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:

1 221,023,103
-1 -221,023,103

Let's try dividing by 4:

221,023,103 ÷ 4 = 55,255,775.75

If the quotient is a whole number, then 4 and 55,255,775.75 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:

1 221,023,103
-1 221,023,103
Keep dividing by the next highest number until you cannot divide anymore.

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

17171195633,2993,9419,57123,09356,08366,997392,5811,857,33713,001,35931,574,729221,023,103
-1-7-17-119-563-3,299-3,941-9,571-23,093-56,083-66,997-392,581-1,857,337-13,001,359-31,574,729-221,023,103

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