Q: What are the factor combinations of the number 12,849,221?

 A:
Positive:   1 x 128492217 x 183560311 x 116811131 x 41449149 x 26222977 x 166873217 x 59213341 x 37681539 x 23839769 x 167091519 x 84592387 x 5383
Negative: -1 x -12849221-7 x -1835603-11 x -1168111-31 x -414491-49 x -262229-77 x -166873-217 x -59213-341 x -37681-539 x -23839-769 x -16709-1519 x -8459-2387 x -5383


How do I find the factor combinations of the number 12,849,221?

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 12,849,221, 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 12,849,221
-1 -12,849,221

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 12,849,221.

Example:
1 x 12,849,221 = 12,849,221
and
-1 x -12,849,221 = 12,849,221
Notice both answers equal 12,849,221

With that explanation out of the way, let's continue. Next, we take the number 12,849,221 and divide it by 2:

12,849,221 ÷ 2 = 6,424,610.5

If the quotient is a whole number, then 2 and 6,424,610.5 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 12,849,221
-1 -12,849,221

Now, we try dividing 12,849,221 by 3:

12,849,221 ÷ 3 = 4,283,073.6667

If the quotient is a whole number, then 3 and 4,283,073.6667 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 12,849,221
-1 -12,849,221

Let's try dividing by 4:

12,849,221 ÷ 4 = 3,212,305.25

If the quotient is a whole number, then 4 and 3,212,305.25 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 12,849,221
-1 12,849,221
Keep dividing by the next highest number until you cannot divide anymore.

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

17113149772173415397691,5192,3875,3838,45916,70923,83937,68159,213166,873262,229414,4911,168,1111,835,60312,849,221
-1-7-11-31-49-77-217-341-539-769-1,519-2,387-5,383-8,459-16,709-23,839-37,681-59,213-166,873-262,229-414,491-1,168,111-1,835,603-12,849,221

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