Q: What are the factor combinations of the number 223,421,365?

 A:
Positive:   1 x 2234213655 x 4468427329 x 7704185145 x 15408371039 x 2150351483 x 1506555195 x 430077415 x 30131
Negative: -1 x -223421365-5 x -44684273-29 x -7704185-145 x -1540837-1039 x -215035-1483 x -150655-5195 x -43007-7415 x -30131


How do I find the factor combinations of the number 223,421,365?

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 223,421,365, 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.

1 223,421,365
-1 -223,421,365

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 223,421,365.

Example:
1 x 223,421,365 = 223,421,365
and
-1 x -223,421,365 = 223,421,365
Notice both answers equal 223,421,365

With that explanation out of the way, let's continue. Next, we take the number 223,421,365 and divide it by 2:

223,421,365 ÷ 2 = 111,710,682.5

If the quotient is a whole number, then 2 and 111,710,682.5 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:

1 223,421,365
-1 -223,421,365

Now, we try dividing 223,421,365 by 3:

223,421,365 ÷ 3 = 74,473,788.3333

If the quotient is a whole number, then 3 and 74,473,788.3333 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:

1 223,421,365
-1 -223,421,365

Let's try dividing by 4:

223,421,365 ÷ 4 = 55,855,341.25

If the quotient is a whole number, then 4 and 55,855,341.25 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:

1 223,421,365
-1 223,421,365
Keep dividing by the next highest number until you cannot divide anymore.

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

15291451,0391,4835,1957,41530,13143,007150,655215,0351,540,8377,704,18544,684,273223,421,365
-1-5-29-145-1,039-1,483-5,195-7,415-30,131-43,007-150,655-215,035-1,540,837-7,704,185-44,684,273-223,421,365

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