Q: What are the factor combinations of the number 12,351,367?

 A:
Positive:   1 x 123513677 x 176448117 x 726551119 x 103793271 x 45577383 x 322491897 x 65112681 x 4607
Negative: -1 x -12351367-7 x -1764481-17 x -726551-119 x -103793-271 x -45577-383 x -32249-1897 x -6511-2681 x -4607


How do I find the factor combinations of the number 12,351,367?

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 12,351,367, 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 12,351,367
-1 -12,351,367

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 12,351,367.

Example:
1 x 12,351,367 = 12,351,367
and
-1 x -12,351,367 = 12,351,367
Notice both answers equal 12,351,367

With that explanation out of the way, let's continue. Next, we take the number 12,351,367 and divide it by 2:

12,351,367 ÷ 2 = 6,175,683.5

If the quotient is a whole number, then 2 and 6,175,683.5 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 12,351,367
-1 -12,351,367

Now, we try dividing 12,351,367 by 3:

12,351,367 ÷ 3 = 4,117,122.3333

If the quotient is a whole number, then 3 and 4,117,122.3333 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 12,351,367
-1 -12,351,367

Let's try dividing by 4:

12,351,367 ÷ 4 = 3,087,841.75

If the quotient is a whole number, then 4 and 3,087,841.75 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 12,351,367
-1 12,351,367
Keep dividing by the next highest number until you cannot divide anymore.

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

17171192713831,8972,6814,6076,51132,24945,577103,793726,5511,764,48112,351,367
-1-7-17-119-271-383-1,897-2,681-4,607-6,511-32,249-45,577-103,793-726,551-1,764,481-12,351,367

More Examples

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