Q: What are the factor combinations of the number 21,653,621?

 A:
Positive:   1 x 2165362111 x 196851137 x 58523383 x 260887407 x 53203641 x 33781913 x 237173071 x 7051
Negative: -1 x -21653621-11 x -1968511-37 x -585233-83 x -260887-407 x -53203-641 x -33781-913 x -23717-3071 x -7051


How do I find the factor combinations of the number 21,653,621?

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 21,653,621, 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 21,653,621
-1 -21,653,621

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 21,653,621.

Example:
1 x 21,653,621 = 21,653,621
and
-1 x -21,653,621 = 21,653,621
Notice both answers equal 21,653,621

With that explanation out of the way, let's continue. Next, we take the number 21,653,621 and divide it by 2:

21,653,621 ÷ 2 = 10,826,810.5

If the quotient is a whole number, then 2 and 10,826,810.5 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 21,653,621
-1 -21,653,621

Now, we try dividing 21,653,621 by 3:

21,653,621 ÷ 3 = 7,217,873.6667

If the quotient is a whole number, then 3 and 7,217,873.6667 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 21,653,621
-1 -21,653,621

Let's try dividing by 4:

21,653,621 ÷ 4 = 5,413,405.25

If the quotient is a whole number, then 4 and 5,413,405.25 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 21,653,621
-1 21,653,621
Keep dividing by the next highest number until you cannot divide anymore.

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

11137834076419133,0717,05123,71733,78153,203260,887585,2331,968,51121,653,621
-1-11-37-83-407-641-913-3,071-7,051-23,717-33,781-53,203-260,887-585,233-1,968,511-21,653,621

More Examples

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