Q: What are the factor combinations of the number 2,210,021?

 A:
Positive:   1 x 221002111 x 20091131 x 71291341 x 6481
Negative: -1 x -2210021-11 x -200911-31 x -71291-341 x -6481


How do I find the factor combinations of the number 2,210,021?

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 2,210,021, 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 2,210,021
-1 -2,210,021

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 2,210,021.

Example:
1 x 2,210,021 = 2,210,021
and
-1 x -2,210,021 = 2,210,021
Notice both answers equal 2,210,021

With that explanation out of the way, let's continue. Next, we take the number 2,210,021 and divide it by 2:

2,210,021 ÷ 2 = 1,105,010.5

If the quotient is a whole number, then 2 and 1,105,010.5 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 2,210,021
-1 -2,210,021

Now, we try dividing 2,210,021 by 3:

2,210,021 ÷ 3 = 736,673.6667

If the quotient is a whole number, then 3 and 736,673.6667 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 2,210,021
-1 -2,210,021

Let's try dividing by 4:

2,210,021 ÷ 4 = 552,505.25

If the quotient is a whole number, then 4 and 552,505.25 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 2,210,021
-1 2,210,021
Keep dividing by the next highest number until you cannot divide anymore.

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

111313416,48171,291200,9112,210,021
-1-11-31-341-6,481-71,291-200,911-2,210,021

More Examples

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