Q: What are the factor combinations of the number 21,354,215?

 A:
Positive:   1 x 213542155 x 427084347 x 45434589 x 239935235 x 90869445 x 479871021 x 209154183 x 5105
Negative: -1 x -21354215-5 x -4270843-47 x -454345-89 x -239935-235 x -90869-445 x -47987-1021 x -20915-4183 x -5105


How do I find the factor combinations of the number 21,354,215?

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 21,354,215, 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 21,354,215
-1 -21,354,215

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 21,354,215.

Example:
1 x 21,354,215 = 21,354,215
and
-1 x -21,354,215 = 21,354,215
Notice both answers equal 21,354,215

With that explanation out of the way, let's continue. Next, we take the number 21,354,215 and divide it by 2:

21,354,215 ÷ 2 = 10,677,107.5

If the quotient is a whole number, then 2 and 10,677,107.5 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 21,354,215
-1 -21,354,215

Now, we try dividing 21,354,215 by 3:

21,354,215 ÷ 3 = 7,118,071.6667

If the quotient is a whole number, then 3 and 7,118,071.6667 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 21,354,215
-1 -21,354,215

Let's try dividing by 4:

21,354,215 ÷ 4 = 5,338,553.75

If the quotient is a whole number, then 4 and 5,338,553.75 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 21,354,215
-1 21,354,215
Keep dividing by the next highest number until you cannot divide anymore.

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

1547892354451,0214,1835,10520,91547,98790,869239,935454,3454,270,84321,354,215
-1-5-47-89-235-445-1,021-4,183-5,105-20,915-47,987-90,869-239,935-454,345-4,270,843-21,354,215

More Examples

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