Q: What are the factor combinations of the number 221,345,231?

 A:
Positive:   1 x 22134523119 x 1164974947 x 4709473311 x 711721797 x 277723893 x 2478675909 x 3745914617 x 15143
Negative: -1 x -221345231-19 x -11649749-47 x -4709473-311 x -711721-797 x -277723-893 x -247867-5909 x -37459-14617 x -15143


How do I find the factor combinations of the number 221,345,231?

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 221,345,231, 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.

1 221,345,231
-1 -221,345,231

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 221,345,231.

Example:
1 x 221,345,231 = 221,345,231
and
-1 x -221,345,231 = 221,345,231
Notice both answers equal 221,345,231

With that explanation out of the way, let's continue. Next, we take the number 221,345,231 and divide it by 2:

221,345,231 ÷ 2 = 110,672,615.5

If the quotient is a whole number, then 2 and 110,672,615.5 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:

1 221,345,231
-1 -221,345,231

Now, we try dividing 221,345,231 by 3:

221,345,231 ÷ 3 = 73,781,743.6667

If the quotient is a whole number, then 3 and 73,781,743.6667 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:

1 221,345,231
-1 -221,345,231

Let's try dividing by 4:

221,345,231 ÷ 4 = 55,336,307.75

If the quotient is a whole number, then 4 and 55,336,307.75 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:

1 221,345,231
-1 221,345,231
Keep dividing by the next highest number until you cannot divide anymore.

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

119473117978935,90914,61715,14337,459247,867277,723711,7214,709,47311,649,749221,345,231
-1-19-47-311-797-893-5,909-14,617-15,143-37,459-247,867-277,723-711,721-4,709,473-11,649,749-221,345,231

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