Q: What are the factor combinations of the number 20,721,905?

 A:
Positive:   1 x 207219055 x 41443811381 x 150053001 x 6905
Negative: -1 x -20721905-5 x -4144381-1381 x -15005-3001 x -6905


How do I find the factor combinations of the number 20,721,905?

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 20,721,905, 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 20,721,905
-1 -20,721,905

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 20,721,905.

Example:
1 x 20,721,905 = 20,721,905
and
-1 x -20,721,905 = 20,721,905
Notice both answers equal 20,721,905

With that explanation out of the way, let's continue. Next, we take the number 20,721,905 and divide it by 2:

20,721,905 ÷ 2 = 10,360,952.5

If the quotient is a whole number, then 2 and 10,360,952.5 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 20,721,905
-1 -20,721,905

Now, we try dividing 20,721,905 by 3:

20,721,905 ÷ 3 = 6,907,301.6667

If the quotient is a whole number, then 3 and 6,907,301.6667 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 20,721,905
-1 -20,721,905

Let's try dividing by 4:

20,721,905 ÷ 4 = 5,180,476.25

If the quotient is a whole number, then 4 and 5,180,476.25 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 20,721,905
-1 20,721,905
Keep dividing by the next highest number until you cannot divide anymore.

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

151,3813,0016,90515,0054,144,38120,721,905
-1-5-1,381-3,001-6,905-15,005-4,144,381-20,721,905

More Examples

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