Q: What are the factor combinations of the number 21,217,361?

 A:
Positive:   1 x 2121736111 x 192885131 x 68443143 x 493427341 x 62221473 x 448571333 x 159171447 x 14663
Negative: -1 x -21217361-11 x -1928851-31 x -684431-43 x -493427-341 x -62221-473 x -44857-1333 x -15917-1447 x -14663


How do I find the factor combinations of the number 21,217,361?

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 21,217,361, 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 21,217,361
-1 -21,217,361

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 21,217,361.

Example:
1 x 21,217,361 = 21,217,361
and
-1 x -21,217,361 = 21,217,361
Notice both answers equal 21,217,361

With that explanation out of the way, let's continue. Next, we take the number 21,217,361 and divide it by 2:

21,217,361 ÷ 2 = 10,608,680.5

If the quotient is a whole number, then 2 and 10,608,680.5 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 21,217,361
-1 -21,217,361

Now, we try dividing 21,217,361 by 3:

21,217,361 ÷ 3 = 7,072,453.6667

If the quotient is a whole number, then 3 and 7,072,453.6667 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 21,217,361
-1 -21,217,361

Let's try dividing by 4:

21,217,361 ÷ 4 = 5,304,340.25

If the quotient is a whole number, then 4 and 5,304,340.25 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 21,217,361
-1 21,217,361
Keep dividing by the next highest number until you cannot divide anymore.

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

11131433414731,3331,44714,66315,91744,85762,221493,427684,4311,928,85121,217,361
-1-11-31-43-341-473-1,333-1,447-14,663-15,917-44,857-62,221-493,427-684,431-1,928,851-21,217,361

More Examples

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