Q: What are the factor combinations of the number 213,103,033?

 A:
Positive:   1 x 21310303311 x 1937300313 x 16392541143 x 1490231449 x 4746173319 x 642074939 x 431475837 x 36509
Negative: -1 x -213103033-11 x -19373003-13 x -16392541-143 x -1490231-449 x -474617-3319 x -64207-4939 x -43147-5837 x -36509


How do I find the factor combinations of the number 213,103,033?

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 213,103,033, 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.

1 213,103,033
-1 -213,103,033

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 213,103,033.

Example:
1 x 213,103,033 = 213,103,033
and
-1 x -213,103,033 = 213,103,033
Notice both answers equal 213,103,033

With that explanation out of the way, let's continue. Next, we take the number 213,103,033 and divide it by 2:

213,103,033 ÷ 2 = 106,551,516.5

If the quotient is a whole number, then 2 and 106,551,516.5 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:

1 213,103,033
-1 -213,103,033

Now, we try dividing 213,103,033 by 3:

213,103,033 ÷ 3 = 71,034,344.3333

If the quotient is a whole number, then 3 and 71,034,344.3333 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:

1 213,103,033
-1 -213,103,033

Let's try dividing by 4:

213,103,033 ÷ 4 = 53,275,758.25

If the quotient is a whole number, then 4 and 53,275,758.25 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:

1 213,103,033
-1 213,103,033
Keep dividing by the next highest number until you cannot divide anymore.

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

111131434493,3194,9395,83736,50943,14764,207474,6171,490,23116,392,54119,373,003213,103,033
-1-11-13-143-449-3,319-4,939-5,837-36,509-43,147-64,207-474,617-1,490,231-16,392,541-19,373,003-213,103,033

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