Q: What are the factor combinations of the number 21,516,845?

 A:
Positive:   1 x 215168455 x 43033697 x 307383523 x 93551535 x 614767115 x 187103161 x 133645805 x 26729
Negative: -1 x -21516845-5 x -4303369-7 x -3073835-23 x -935515-35 x -614767-115 x -187103-161 x -133645-805 x -26729


How do I find the factor combinations of the number 21,516,845?

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 21,516,845, 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 21,516,845
-1 -21,516,845

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 21,516,845.

Example:
1 x 21,516,845 = 21,516,845
and
-1 x -21,516,845 = 21,516,845
Notice both answers equal 21,516,845

With that explanation out of the way, let's continue. Next, we take the number 21,516,845 and divide it by 2:

21,516,845 ÷ 2 = 10,758,422.5

If the quotient is a whole number, then 2 and 10,758,422.5 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 21,516,845
-1 -21,516,845

Now, we try dividing 21,516,845 by 3:

21,516,845 ÷ 3 = 7,172,281.6667

If the quotient is a whole number, then 3 and 7,172,281.6667 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 21,516,845
-1 -21,516,845

Let's try dividing by 4:

21,516,845 ÷ 4 = 5,379,211.25

If the quotient is a whole number, then 4 and 5,379,211.25 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 21,516,845
-1 21,516,845
Keep dividing by the next highest number until you cannot divide anymore.

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

157233511516180526,729133,645187,103614,767935,5153,073,8354,303,36921,516,845
-1-5-7-23-35-115-161-805-26,729-133,645-187,103-614,767-935,515-3,073,835-4,303,369-21,516,845

More Examples

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