Q: What are the factor combinations of the number 223,300,321?

 A:
Positive:   1 x 22330032117 x 1313531361 x 3660661349 x 639829617 x 3619131037 x 2153335933 x 3763710489 x 21289
Negative: -1 x -223300321-17 x -13135313-61 x -3660661-349 x -639829-617 x -361913-1037 x -215333-5933 x -37637-10489 x -21289


How do I find the factor combinations of the number 223,300,321?

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 223,300,321, 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.

1 223,300,321
-1 -223,300,321

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 223,300,321.

Example:
1 x 223,300,321 = 223,300,321
and
-1 x -223,300,321 = 223,300,321
Notice both answers equal 223,300,321

With that explanation out of the way, let's continue. Next, we take the number 223,300,321 and divide it by 2:

223,300,321 ÷ 2 = 111,650,160.5

If the quotient is a whole number, then 2 and 111,650,160.5 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:

1 223,300,321
-1 -223,300,321

Now, we try dividing 223,300,321 by 3:

223,300,321 ÷ 3 = 74,433,440.3333

If the quotient is a whole number, then 3 and 74,433,440.3333 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:

1 223,300,321
-1 -223,300,321

Let's try dividing by 4:

223,300,321 ÷ 4 = 55,825,080.25

If the quotient is a whole number, then 4 and 55,825,080.25 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:

1 223,300,321
-1 223,300,321
Keep dividing by the next highest number until you cannot divide anymore.

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

117613496171,0375,93310,48921,28937,637215,333361,913639,8293,660,66113,135,313223,300,321
-1-17-61-349-617-1,037-5,933-10,489-21,289-37,637-215,333-361,913-639,829-3,660,661-13,135,313-223,300,321

More Examples

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