Q: What are the factor combinations of the number 12,171,635?

 A:
Positive:   1 x 121716355 x 24343277 x 173880535 x 34776161 x 199535305 x 39907427 x 285052135 x 5701
Negative: -1 x -12171635-5 x -2434327-7 x -1738805-35 x -347761-61 x -199535-305 x -39907-427 x -28505-2135 x -5701


How do I find the factor combinations of the number 12,171,635?

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 12,171,635, 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 12,171,635
-1 -12,171,635

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 12,171,635.

Example:
1 x 12,171,635 = 12,171,635
and
-1 x -12,171,635 = 12,171,635
Notice both answers equal 12,171,635

With that explanation out of the way, let's continue. Next, we take the number 12,171,635 and divide it by 2:

12,171,635 ÷ 2 = 6,085,817.5

If the quotient is a whole number, then 2 and 6,085,817.5 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 12,171,635
-1 -12,171,635

Now, we try dividing 12,171,635 by 3:

12,171,635 ÷ 3 = 4,057,211.6667

If the quotient is a whole number, then 3 and 4,057,211.6667 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 12,171,635
-1 -12,171,635

Let's try dividing by 4:

12,171,635 ÷ 4 = 3,042,908.75

If the quotient is a whole number, then 4 and 3,042,908.75 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 12,171,635
-1 12,171,635
Keep dividing by the next highest number until you cannot divide anymore.

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

15735613054272,1355,70128,50539,907199,535347,7611,738,8052,434,32712,171,635
-1-5-7-35-61-305-427-2,135-5,701-28,505-39,907-199,535-347,761-1,738,805-2,434,327-12,171,635

More Examples

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