Q: What are the factor combinations of the number 21,500,796?

 A:
Positive:   1 x 215007962 x 107503983 x 71669324 x 53751996 x 358346612 x 1791733
Negative: -1 x -21500796-2 x -10750398-3 x -7166932-4 x -5375199-6 x -3583466-12 x -1791733


How do I find the factor combinations of the number 21,500,796?

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 21,500,796, 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 21,500,796
-1 -21,500,796

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 21,500,796.

Example:
1 x 21,500,796 = 21,500,796
and
-1 x -21,500,796 = 21,500,796
Notice both answers equal 21,500,796

With that explanation out of the way, let's continue. Next, we take the number 21,500,796 and divide it by 2:

21,500,796 ÷ 2 = 10,750,398

If the quotient is a whole number, then 2 and 10,750,398 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 10,750,398 21,500,796
-1 -2 -10,750,398 -21,500,796

Now, we try dividing 21,500,796 by 3:

21,500,796 ÷ 3 = 7,166,932

If the quotient is a whole number, then 3 and 7,166,932 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 7,166,932 10,750,398 21,500,796
-1 -2 -3 -7,166,932 -10,750,398 -21,500,796

Let's try dividing by 4:

21,500,796 ÷ 4 = 5,375,199

If the quotient is a whole number, then 4 and 5,375,199 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 5,375,199 7,166,932 10,750,398 21,500,796
-1 -2 -3 -4 -5,375,199 -7,166,932 -10,750,398 21,500,796
Keep dividing by the next highest number until you cannot divide anymore.

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

12346121,791,7333,583,4665,375,1997,166,93210,750,39821,500,796
-1-2-3-4-6-12-1,791,733-3,583,466-5,375,199-7,166,932-10,750,398-21,500,796

More Examples

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