Q: What are the factor combinations of the number 212,072,707?

 A:
Positive:   1 x 2120727077 x 3029610111 x 1927933777 x 2754191121 x 1752667227 x 934241847 x 2503811103 x 1922691589 x 1334632497 x 849317721 x 2746712133 x 17479
Negative: -1 x -212072707-7 x -30296101-11 x -19279337-77 x -2754191-121 x -1752667-227 x -934241-847 x -250381-1103 x -192269-1589 x -133463-2497 x -84931-7721 x -27467-12133 x -17479


How do I find the factor combinations of the number 212,072,707?

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 212,072,707, 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.

1 212,072,707
-1 -212,072,707

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 212,072,707.

Example:
1 x 212,072,707 = 212,072,707
and
-1 x -212,072,707 = 212,072,707
Notice both answers equal 212,072,707

With that explanation out of the way, let's continue. Next, we take the number 212,072,707 and divide it by 2:

212,072,707 ÷ 2 = 106,036,353.5

If the quotient is a whole number, then 2 and 106,036,353.5 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:

1 212,072,707
-1 -212,072,707

Now, we try dividing 212,072,707 by 3:

212,072,707 ÷ 3 = 70,690,902.3333

If the quotient is a whole number, then 3 and 70,690,902.3333 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:

1 212,072,707
-1 -212,072,707

Let's try dividing by 4:

212,072,707 ÷ 4 = 53,018,176.75

If the quotient is a whole number, then 4 and 53,018,176.75 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:

1 212,072,707
-1 212,072,707
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771212278471,1031,5892,4977,72112,13317,47927,46784,931133,463192,269250,381934,2411,752,6672,754,19119,279,33730,296,101212,072,707
-1-7-11-77-121-227-847-1,103-1,589-2,497-7,721-12,133-17,479-27,467-84,931-133,463-192,269-250,381-934,241-1,752,667-2,754,191-19,279,337-30,296,101-212,072,707

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