Q: What are the factor combinations of the number 21,604,121?

 A:
Positive:   1 x 216041217 x 308630311 x 196401119 x 113705977 x 280573133 x 162437209 x 1033691463 x 14767
Negative: -1 x -21604121-7 x -3086303-11 x -1964011-19 x -1137059-77 x -280573-133 x -162437-209 x -103369-1463 x -14767


How do I find the factor combinations of the number 21,604,121?

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 21,604,121, 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 21,604,121
-1 -21,604,121

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 21,604,121.

Example:
1 x 21,604,121 = 21,604,121
and
-1 x -21,604,121 = 21,604,121
Notice both answers equal 21,604,121

With that explanation out of the way, let's continue. Next, we take the number 21,604,121 and divide it by 2:

21,604,121 ÷ 2 = 10,802,060.5

If the quotient is a whole number, then 2 and 10,802,060.5 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 21,604,121
-1 -21,604,121

Now, we try dividing 21,604,121 by 3:

21,604,121 ÷ 3 = 7,201,373.6667

If the quotient is a whole number, then 3 and 7,201,373.6667 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 21,604,121
-1 -21,604,121

Let's try dividing by 4:

21,604,121 ÷ 4 = 5,401,030.25

If the quotient is a whole number, then 4 and 5,401,030.25 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 21,604,121
-1 21,604,121
Keep dividing by the next highest number until you cannot divide anymore.

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

171119771332091,46314,767103,369162,437280,5731,137,0591,964,0113,086,30321,604,121
-1-7-11-19-77-133-209-1,463-14,767-103,369-162,437-280,573-1,137,059-1,964,011-3,086,303-21,604,121

More Examples

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