Q: What are the factor combinations of the number 21,215,105?

 A:
Positive:   1 x 212151055 x 424302153 x 400285223 x 95135265 x 80057359 x 590951115 x 190271795 x 11819
Negative: -1 x -21215105-5 x -4243021-53 x -400285-223 x -95135-265 x -80057-359 x -59095-1115 x -19027-1795 x -11819


How do I find the factor combinations of the number 21,215,105?

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 21,215,105, 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 21,215,105
-1 -21,215,105

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 21,215,105.

Example:
1 x 21,215,105 = 21,215,105
and
-1 x -21,215,105 = 21,215,105
Notice both answers equal 21,215,105

With that explanation out of the way, let's continue. Next, we take the number 21,215,105 and divide it by 2:

21,215,105 ÷ 2 = 10,607,552.5

If the quotient is a whole number, then 2 and 10,607,552.5 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 21,215,105
-1 -21,215,105

Now, we try dividing 21,215,105 by 3:

21,215,105 ÷ 3 = 7,071,701.6667

If the quotient is a whole number, then 3 and 7,071,701.6667 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 21,215,105
-1 -21,215,105

Let's try dividing by 4:

21,215,105 ÷ 4 = 5,303,776.25

If the quotient is a whole number, then 4 and 5,303,776.25 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 21,215,105
-1 21,215,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15532232653591,1151,79511,81919,02759,09580,05795,135400,2854,243,02121,215,105
-1-5-53-223-265-359-1,115-1,795-11,819-19,027-59,095-80,057-95,135-400,285-4,243,021-21,215,105

More Examples

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