Q: What are the factor combinations of the number 12,228,229?

 A:
Positive:   1 x 1222822913 x 94063319 x 64359131 x 394459247 x 49507403 x 30343589 x 207611597 x 7657
Negative: -1 x -12228229-13 x -940633-19 x -643591-31 x -394459-247 x -49507-403 x -30343-589 x -20761-1597 x -7657


How do I find the factor combinations of the number 12,228,229?

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 12,228,229, 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 12,228,229
-1 -12,228,229

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 12,228,229.

Example:
1 x 12,228,229 = 12,228,229
and
-1 x -12,228,229 = 12,228,229
Notice both answers equal 12,228,229

With that explanation out of the way, let's continue. Next, we take the number 12,228,229 and divide it by 2:

12,228,229 ÷ 2 = 6,114,114.5

If the quotient is a whole number, then 2 and 6,114,114.5 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 12,228,229
-1 -12,228,229

Now, we try dividing 12,228,229 by 3:

12,228,229 ÷ 3 = 4,076,076.3333

If the quotient is a whole number, then 3 and 4,076,076.3333 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 12,228,229
-1 -12,228,229

Let's try dividing by 4:

12,228,229 ÷ 4 = 3,057,057.25

If the quotient is a whole number, then 4 and 3,057,057.25 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 12,228,229
-1 12,228,229
Keep dividing by the next highest number until you cannot divide anymore.

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

11319312474035891,5977,65720,76130,34349,507394,459643,591940,63312,228,229
-1-13-19-31-247-403-589-1,597-7,657-20,761-30,343-49,507-394,459-643,591-940,633-12,228,229

More Examples

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