Q: What are the factor combinations of the number 213,210,127?

 A:
Positive:   1 x 21321012713 x 1640077941 x 5200247337 x 632671533 x 4000191187 x 1796214381 x 4866713817 x 15431
Negative: -1 x -213210127-13 x -16400779-41 x -5200247-337 x -632671-533 x -400019-1187 x -179621-4381 x -48667-13817 x -15431


How do I find the factor combinations of the number 213,210,127?

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 213,210,127, 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.

1 213,210,127
-1 -213,210,127

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 213,210,127.

Example:
1 x 213,210,127 = 213,210,127
and
-1 x -213,210,127 = 213,210,127
Notice both answers equal 213,210,127

With that explanation out of the way, let's continue. Next, we take the number 213,210,127 and divide it by 2:

213,210,127 ÷ 2 = 106,605,063.5

If the quotient is a whole number, then 2 and 106,605,063.5 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:

1 213,210,127
-1 -213,210,127

Now, we try dividing 213,210,127 by 3:

213,210,127 ÷ 3 = 71,070,042.3333

If the quotient is a whole number, then 3 and 71,070,042.3333 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:

1 213,210,127
-1 -213,210,127

Let's try dividing by 4:

213,210,127 ÷ 4 = 53,302,531.75

If the quotient is a whole number, then 4 and 53,302,531.75 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:

1 213,210,127
-1 213,210,127
Keep dividing by the next highest number until you cannot divide anymore.

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

113413375331,1874,38113,81715,43148,667179,621400,019632,6715,200,24716,400,779213,210,127
-1-13-41-337-533-1,187-4,381-13,817-15,431-48,667-179,621-400,019-632,671-5,200,247-16,400,779-213,210,127

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