Q: What are the factor combinations of the number 210,200,441?

 A:
Positive:   1 x 21020044111 x 1910913137 x 5681093241 x 872201407 x 5164632143 x 980872651 x 792918917 x 23573
Negative: -1 x -210200441-11 x -19109131-37 x -5681093-241 x -872201-407 x -516463-2143 x -98087-2651 x -79291-8917 x -23573


How do I find the factor combinations of the number 210,200,441?

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 210,200,441, 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.

1 210,200,441
-1 -210,200,441

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 210,200,441.

Example:
1 x 210,200,441 = 210,200,441
and
-1 x -210,200,441 = 210,200,441
Notice both answers equal 210,200,441

With that explanation out of the way, let's continue. Next, we take the number 210,200,441 and divide it by 2:

210,200,441 ÷ 2 = 105,100,220.5

If the quotient is a whole number, then 2 and 105,100,220.5 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:

1 210,200,441
-1 -210,200,441

Now, we try dividing 210,200,441 by 3:

210,200,441 ÷ 3 = 70,066,813.6667

If the quotient is a whole number, then 3 and 70,066,813.6667 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:

1 210,200,441
-1 -210,200,441

Let's try dividing by 4:

210,200,441 ÷ 4 = 52,550,110.25

If the quotient is a whole number, then 4 and 52,550,110.25 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:

1 210,200,441
-1 210,200,441
Keep dividing by the next highest number until you cannot divide anymore.

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

111372414072,1432,6518,91723,57379,29198,087516,463872,2015,681,09319,109,131210,200,441
-1-11-37-241-407-2,143-2,651-8,917-23,573-79,291-98,087-516,463-872,201-5,681,093-19,109,131-210,200,441

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