Q: What are the factor combinations of the number 21,210,395?

 A:
Positive:   1 x 212103955 x 424207943 x 49326547 x 451285215 x 98653235 x 902572021 x 104952099 x 10105
Negative: -1 x -21210395-5 x -4242079-43 x -493265-47 x -451285-215 x -98653-235 x -90257-2021 x -10495-2099 x -10105


How do I find the factor combinations of the number 21,210,395?

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 21,210,395, 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 21,210,395
-1 -21,210,395

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 21,210,395.

Example:
1 x 21,210,395 = 21,210,395
and
-1 x -21,210,395 = 21,210,395
Notice both answers equal 21,210,395

With that explanation out of the way, let's continue. Next, we take the number 21,210,395 and divide it by 2:

21,210,395 ÷ 2 = 10,605,197.5

If the quotient is a whole number, then 2 and 10,605,197.5 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 21,210,395
-1 -21,210,395

Now, we try dividing 21,210,395 by 3:

21,210,395 ÷ 3 = 7,070,131.6667

If the quotient is a whole number, then 3 and 7,070,131.6667 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 21,210,395
-1 -21,210,395

Let's try dividing by 4:

21,210,395 ÷ 4 = 5,302,598.75

If the quotient is a whole number, then 4 and 5,302,598.75 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 21,210,395
-1 21,210,395
Keep dividing by the next highest number until you cannot divide anymore.

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

1543472152352,0212,09910,10510,49590,25798,653451,285493,2654,242,07921,210,395
-1-5-43-47-215-235-2,021-2,099-10,105-10,495-90,257-98,653-451,285-493,265-4,242,079-21,210,395

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