Q: What are the factor combinations of the number 213,422,407?

 A:
Positive:   1 x 21342240711 x 1940203797 x 2200231139 x 15354131067 x 2000211439 x 1483131529 x 13958313483 x 15829
Negative: -1 x -213422407-11 x -19402037-97 x -2200231-139 x -1535413-1067 x -200021-1439 x -148313-1529 x -139583-13483 x -15829


How do I find the factor combinations of the number 213,422,407?

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 213,422,407, 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.

1 213,422,407
-1 -213,422,407

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 213,422,407.

Example:
1 x 213,422,407 = 213,422,407
and
-1 x -213,422,407 = 213,422,407
Notice both answers equal 213,422,407

With that explanation out of the way, let's continue. Next, we take the number 213,422,407 and divide it by 2:

213,422,407 ÷ 2 = 106,711,203.5

If the quotient is a whole number, then 2 and 106,711,203.5 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:

1 213,422,407
-1 -213,422,407

Now, we try dividing 213,422,407 by 3:

213,422,407 ÷ 3 = 71,140,802.3333

If the quotient is a whole number, then 3 and 71,140,802.3333 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:

1 213,422,407
-1 -213,422,407

Let's try dividing by 4:

213,422,407 ÷ 4 = 53,355,601.75

If the quotient is a whole number, then 4 and 53,355,601.75 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:

1 213,422,407
-1 213,422,407
Keep dividing by the next highest number until you cannot divide anymore.

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

111971391,0671,4391,52913,48315,829139,583148,313200,0211,535,4132,200,23119,402,037213,422,407
-1-11-97-139-1,067-1,439-1,529-13,483-15,829-139,583-148,313-200,021-1,535,413-2,200,231-19,402,037-213,422,407

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