Q: What are the factor combinations of the number 210,050,203?

 A:
Positive:   1 x 21005020311 x 1909547331 x 6775813271 x 775093341 x 6159832273 x 924112981 x 704638401 x 25003
Negative: -1 x -210050203-11 x -19095473-31 x -6775813-271 x -775093-341 x -615983-2273 x -92411-2981 x -70463-8401 x -25003


How do I find the factor combinations of the number 210,050,203?

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 210,050,203, 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.

1 210,050,203
-1 -210,050,203

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 210,050,203.

Example:
1 x 210,050,203 = 210,050,203
and
-1 x -210,050,203 = 210,050,203
Notice both answers equal 210,050,203

With that explanation out of the way, let's continue. Next, we take the number 210,050,203 and divide it by 2:

210,050,203 ÷ 2 = 105,025,101.5

If the quotient is a whole number, then 2 and 105,025,101.5 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:

1 210,050,203
-1 -210,050,203

Now, we try dividing 210,050,203 by 3:

210,050,203 ÷ 3 = 70,016,734.3333

If the quotient is a whole number, then 3 and 70,016,734.3333 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:

1 210,050,203
-1 -210,050,203

Let's try dividing by 4:

210,050,203 ÷ 4 = 52,512,550.75

If the quotient is a whole number, then 4 and 52,512,550.75 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:

1 210,050,203
-1 210,050,203
Keep dividing by the next highest number until you cannot divide anymore.

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

111312713412,2732,9818,40125,00370,46392,411615,983775,0936,775,81319,095,473210,050,203
-1-11-31-271-341-2,273-2,981-8,401-25,003-70,463-92,411-615,983-775,093-6,775,813-19,095,473-210,050,203

More Examples

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