Q: What are the factor combinations of the number 13,022,233?

 A:
Positive:   1 x 130222337 x 1860319101 x 128933113 x 115241163 x 79891707 x 18419791 x 164631141 x 11413
Negative: -1 x -13022233-7 x -1860319-101 x -128933-113 x -115241-163 x -79891-707 x -18419-791 x -16463-1141 x -11413


How do I find the factor combinations of the number 13,022,233?

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 13,022,233, 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 13,022,233
-1 -13,022,233

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 13,022,233.

Example:
1 x 13,022,233 = 13,022,233
and
-1 x -13,022,233 = 13,022,233
Notice both answers equal 13,022,233

With that explanation out of the way, let's continue. Next, we take the number 13,022,233 and divide it by 2:

13,022,233 ÷ 2 = 6,511,116.5

If the quotient is a whole number, then 2 and 6,511,116.5 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 13,022,233
-1 -13,022,233

Now, we try dividing 13,022,233 by 3:

13,022,233 ÷ 3 = 4,340,744.3333

If the quotient is a whole number, then 3 and 4,340,744.3333 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 13,022,233
-1 -13,022,233

Let's try dividing by 4:

13,022,233 ÷ 4 = 3,255,558.25

If the quotient is a whole number, then 4 and 3,255,558.25 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 13,022,233
-1 13,022,233
Keep dividing by the next highest number until you cannot divide anymore.

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

171011131637077911,14111,41316,46318,41979,891115,241128,9331,860,31913,022,233
-1-7-101-113-163-707-791-1,141-11,413-16,463-18,419-79,891-115,241-128,933-1,860,319-13,022,233

More Examples

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