Q: What are the factor combinations of the number 213,018,673?

 A:
Positive:   1 x 2130186737 x 3043123971 x 3000263113 x 1885121497 x 428609791 x 2693033793 x 561618023 x 26551
Negative: -1 x -213018673-7 x -30431239-71 x -3000263-113 x -1885121-497 x -428609-791 x -269303-3793 x -56161-8023 x -26551


How do I find the factor combinations of the number 213,018,673?

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 213,018,673, 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.

1 213,018,673
-1 -213,018,673

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 213,018,673.

Example:
1 x 213,018,673 = 213,018,673
and
-1 x -213,018,673 = 213,018,673
Notice both answers equal 213,018,673

With that explanation out of the way, let's continue. Next, we take the number 213,018,673 and divide it by 2:

213,018,673 ÷ 2 = 106,509,336.5

If the quotient is a whole number, then 2 and 106,509,336.5 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:

1 213,018,673
-1 -213,018,673

Now, we try dividing 213,018,673 by 3:

213,018,673 ÷ 3 = 71,006,224.3333

If the quotient is a whole number, then 3 and 71,006,224.3333 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:

1 213,018,673
-1 -213,018,673

Let's try dividing by 4:

213,018,673 ÷ 4 = 53,254,668.25

If the quotient is a whole number, then 4 and 53,254,668.25 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:

1 213,018,673
-1 213,018,673
Keep dividing by the next highest number until you cannot divide anymore.

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

17711134977913,7938,02326,55156,161269,303428,6091,885,1213,000,26330,431,239213,018,673
-1-7-71-113-497-791-3,793-8,023-26,551-56,161-269,303-428,609-1,885,121-3,000,263-30,431,239-213,018,673

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