Q: What are the factor combinations of the number 12,029,171?

 A:
Positive:   1 x 120291717 x 171845311 x 109356129 x 41479977 x 156223203 x 59257319 x 377092233 x 5387
Negative: -1 x -12029171-7 x -1718453-11 x -1093561-29 x -414799-77 x -156223-203 x -59257-319 x -37709-2233 x -5387


How do I find the factor combinations of the number 12,029,171?

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 12,029,171, 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 12,029,171
-1 -12,029,171

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 12,029,171.

Example:
1 x 12,029,171 = 12,029,171
and
-1 x -12,029,171 = 12,029,171
Notice both answers equal 12,029,171

With that explanation out of the way, let's continue. Next, we take the number 12,029,171 and divide it by 2:

12,029,171 ÷ 2 = 6,014,585.5

If the quotient is a whole number, then 2 and 6,014,585.5 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 12,029,171
-1 -12,029,171

Now, we try dividing 12,029,171 by 3:

12,029,171 ÷ 3 = 4,009,723.6667

If the quotient is a whole number, then 3 and 4,009,723.6667 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 12,029,171
-1 -12,029,171

Let's try dividing by 4:

12,029,171 ÷ 4 = 3,007,292.75

If the quotient is a whole number, then 4 and 3,007,292.75 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 12,029,171
-1 12,029,171
Keep dividing by the next highest number until you cannot divide anymore.

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

171129772033192,2335,38737,70959,257156,223414,7991,093,5611,718,45312,029,171
-1-7-11-29-77-203-319-2,233-5,387-37,709-59,257-156,223-414,799-1,093,561-1,718,453-12,029,171

More Examples

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