Q: What are the factor combinations of the number 221,430,223?

 A:
Positive:   1 x 2214302237 x 3163288923 x 9627401137 x 1616279161 x 1375343959 x 2308973151 x 7027310039 x 22057
Negative: -1 x -221430223-7 x -31632889-23 x -9627401-137 x -1616279-161 x -1375343-959 x -230897-3151 x -70273-10039 x -22057


How do I find the factor combinations of the number 221,430,223?

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 221,430,223, 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.

1 221,430,223
-1 -221,430,223

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 221,430,223.

Example:
1 x 221,430,223 = 221,430,223
and
-1 x -221,430,223 = 221,430,223
Notice both answers equal 221,430,223

With that explanation out of the way, let's continue. Next, we take the number 221,430,223 and divide it by 2:

221,430,223 ÷ 2 = 110,715,111.5

If the quotient is a whole number, then 2 and 110,715,111.5 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:

1 221,430,223
-1 -221,430,223

Now, we try dividing 221,430,223 by 3:

221,430,223 ÷ 3 = 73,810,074.3333

If the quotient is a whole number, then 3 and 73,810,074.3333 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:

1 221,430,223
-1 -221,430,223

Let's try dividing by 4:

221,430,223 ÷ 4 = 55,357,555.75

If the quotient is a whole number, then 4 and 55,357,555.75 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:

1 221,430,223
-1 221,430,223
Keep dividing by the next highest number until you cannot divide anymore.

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

17231371619593,15110,03922,05770,273230,8971,375,3431,616,2799,627,40131,632,889221,430,223
-1-7-23-137-161-959-3,151-10,039-22,057-70,273-230,897-1,375,343-1,616,279-9,627,401-31,632,889-221,430,223

More Examples

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