Q: What are the factor combinations of the number 21,210,301?

 A:
Positive:   1 x 212103017 x 303004323 x 92218747 x 451283161 x 131741329 x 644691081 x 196212803 x 7567
Negative: -1 x -21210301-7 x -3030043-23 x -922187-47 x -451283-161 x -131741-329 x -64469-1081 x -19621-2803 x -7567


How do I find the factor combinations of the number 21,210,301?

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 21,210,301, 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 21,210,301
-1 -21,210,301

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 21,210,301.

Example:
1 x 21,210,301 = 21,210,301
and
-1 x -21,210,301 = 21,210,301
Notice both answers equal 21,210,301

With that explanation out of the way, let's continue. Next, we take the number 21,210,301 and divide it by 2:

21,210,301 ÷ 2 = 10,605,150.5

If the quotient is a whole number, then 2 and 10,605,150.5 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 21,210,301
-1 -21,210,301

Now, we try dividing 21,210,301 by 3:

21,210,301 ÷ 3 = 7,070,100.3333

If the quotient is a whole number, then 3 and 7,070,100.3333 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 21,210,301
-1 -21,210,301

Let's try dividing by 4:

21,210,301 ÷ 4 = 5,302,575.25

If the quotient is a whole number, then 4 and 5,302,575.25 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 21,210,301
-1 21,210,301
Keep dividing by the next highest number until you cannot divide anymore.

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

1723471613291,0812,8037,56719,62164,469131,741451,283922,1873,030,04321,210,301
-1-7-23-47-161-329-1,081-2,803-7,567-19,621-64,469-131,741-451,283-922,187-3,030,043-21,210,301

More Examples

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