Q: What are the factor combinations of the number 212,424,199?

 A:
Positive:   1 x 21242419913 x 1634032319 x 11180221247 x 860017709 x 2996111213 x 1751239217 x 2304713471 x 15769
Negative: -1 x -212424199-13 x -16340323-19 x -11180221-247 x -860017-709 x -299611-1213 x -175123-9217 x -23047-13471 x -15769


How do I find the factor combinations of the number 212,424,199?

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 212,424,199, 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.

1 212,424,199
-1 -212,424,199

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 212,424,199.

Example:
1 x 212,424,199 = 212,424,199
and
-1 x -212,424,199 = 212,424,199
Notice both answers equal 212,424,199

With that explanation out of the way, let's continue. Next, we take the number 212,424,199 and divide it by 2:

212,424,199 ÷ 2 = 106,212,099.5

If the quotient is a whole number, then 2 and 106,212,099.5 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:

1 212,424,199
-1 -212,424,199

Now, we try dividing 212,424,199 by 3:

212,424,199 ÷ 3 = 70,808,066.3333

If the quotient is a whole number, then 3 and 70,808,066.3333 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:

1 212,424,199
-1 -212,424,199

Let's try dividing by 4:

212,424,199 ÷ 4 = 53,106,049.75

If the quotient is a whole number, then 4 and 53,106,049.75 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:

1 212,424,199
-1 212,424,199
Keep dividing by the next highest number until you cannot divide anymore.

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

113192477091,2139,21713,47115,76923,047175,123299,611860,01711,180,22116,340,323212,424,199
-1-13-19-247-709-1,213-9,217-13,471-15,769-23,047-175,123-299,611-860,017-11,180,221-16,340,323-212,424,199

More Examples

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