Q: What are the factor combinations of the number 12,361,105?

 A:
Positive:   1 x 123611055 x 247222129 x 426245145 x 85249163 x 75835523 x 23635815 x 151672615 x 4727
Negative: -1 x -12361105-5 x -2472221-29 x -426245-145 x -85249-163 x -75835-523 x -23635-815 x -15167-2615 x -4727


How do I find the factor combinations of the number 12,361,105?

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 12,361,105, 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 12,361,105
-1 -12,361,105

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 12,361,105.

Example:
1 x 12,361,105 = 12,361,105
and
-1 x -12,361,105 = 12,361,105
Notice both answers equal 12,361,105

With that explanation out of the way, let's continue. Next, we take the number 12,361,105 and divide it by 2:

12,361,105 ÷ 2 = 6,180,552.5

If the quotient is a whole number, then 2 and 6,180,552.5 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 12,361,105
-1 -12,361,105

Now, we try dividing 12,361,105 by 3:

12,361,105 ÷ 3 = 4,120,368.3333

If the quotient is a whole number, then 3 and 4,120,368.3333 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 12,361,105
-1 -12,361,105

Let's try dividing by 4:

12,361,105 ÷ 4 = 3,090,276.25

If the quotient is a whole number, then 4 and 3,090,276.25 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 12,361,105
-1 12,361,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15291451635238152,6154,72715,16723,63575,83585,249426,2452,472,22112,361,105
-1-5-29-145-163-523-815-2,615-4,727-15,167-23,635-75,835-85,249-426,245-2,472,221-12,361,105

More Examples

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