Q: What are the factor combinations of the number 21,607,901?

 A:
Positive:   1 x 216079017 x 308684317 x 1271053107 x 201943119 x 181579749 x 288491697 x 127331819 x 11879
Negative: -1 x -21607901-7 x -3086843-17 x -1271053-107 x -201943-119 x -181579-749 x -28849-1697 x -12733-1819 x -11879


How do I find the factor combinations of the number 21,607,901?

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 21,607,901, 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 21,607,901
-1 -21,607,901

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 21,607,901.

Example:
1 x 21,607,901 = 21,607,901
and
-1 x -21,607,901 = 21,607,901
Notice both answers equal 21,607,901

With that explanation out of the way, let's continue. Next, we take the number 21,607,901 and divide it by 2:

21,607,901 ÷ 2 = 10,803,950.5

If the quotient is a whole number, then 2 and 10,803,950.5 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 21,607,901
-1 -21,607,901

Now, we try dividing 21,607,901 by 3:

21,607,901 ÷ 3 = 7,202,633.6667

If the quotient is a whole number, then 3 and 7,202,633.6667 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 21,607,901
-1 -21,607,901

Let's try dividing by 4:

21,607,901 ÷ 4 = 5,401,975.25

If the quotient is a whole number, then 4 and 5,401,975.25 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 21,607,901
-1 21,607,901
Keep dividing by the next highest number until you cannot divide anymore.

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

17171071197491,6971,81911,87912,73328,849181,579201,9431,271,0533,086,84321,607,901
-1-7-17-107-119-749-1,697-1,819-11,879-12,733-28,849-181,579-201,943-1,271,053-3,086,843-21,607,901

More Examples

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