Q: What are the factor combinations of the number 21,315,665?

 A:
Positive:   1 x 213156655 x 42631337 x 304509535 x 609019131 x 162715655 x 32543917 x 232454585 x 4649
Negative: -1 x -21315665-5 x -4263133-7 x -3045095-35 x -609019-131 x -162715-655 x -32543-917 x -23245-4585 x -4649


How do I find the factor combinations of the number 21,315,665?

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 21,315,665, 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 21,315,665
-1 -21,315,665

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 21,315,665.

Example:
1 x 21,315,665 = 21,315,665
and
-1 x -21,315,665 = 21,315,665
Notice both answers equal 21,315,665

With that explanation out of the way, let's continue. Next, we take the number 21,315,665 and divide it by 2:

21,315,665 ÷ 2 = 10,657,832.5

If the quotient is a whole number, then 2 and 10,657,832.5 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 21,315,665
-1 -21,315,665

Now, we try dividing 21,315,665 by 3:

21,315,665 ÷ 3 = 7,105,221.6667

If the quotient is a whole number, then 3 and 7,105,221.6667 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 21,315,665
-1 -21,315,665

Let's try dividing by 4:

21,315,665 ÷ 4 = 5,328,916.25

If the quotient is a whole number, then 4 and 5,328,916.25 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 21,315,665
-1 21,315,665
Keep dividing by the next highest number until you cannot divide anymore.

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

157351316559174,5854,64923,24532,543162,715609,0193,045,0954,263,13321,315,665
-1-5-7-35-131-655-917-4,585-4,649-23,245-32,543-162,715-609,019-3,045,095-4,263,133-21,315,665

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