Q: What are the factor combinations of the number 21,716,123?

 A:
Positive:   1 x 2171612311 x 197419313 x 167047117 x 1277419143 x 151861187 x 116129221 x 982632431 x 8933
Negative: -1 x -21716123-11 x -1974193-13 x -1670471-17 x -1277419-143 x -151861-187 x -116129-221 x -98263-2431 x -8933


How do I find the factor combinations of the number 21,716,123?

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 21,716,123, 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 21,716,123
-1 -21,716,123

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 21,716,123.

Example:
1 x 21,716,123 = 21,716,123
and
-1 x -21,716,123 = 21,716,123
Notice both answers equal 21,716,123

With that explanation out of the way, let's continue. Next, we take the number 21,716,123 and divide it by 2:

21,716,123 ÷ 2 = 10,858,061.5

If the quotient is a whole number, then 2 and 10,858,061.5 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 21,716,123
-1 -21,716,123

Now, we try dividing 21,716,123 by 3:

21,716,123 ÷ 3 = 7,238,707.6667

If the quotient is a whole number, then 3 and 7,238,707.6667 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 21,716,123
-1 -21,716,123

Let's try dividing by 4:

21,716,123 ÷ 4 = 5,429,030.75

If the quotient is a whole number, then 4 and 5,429,030.75 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 21,716,123
-1 21,716,123
Keep dividing by the next highest number until you cannot divide anymore.

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

11113171431872212,4318,93398,263116,129151,8611,277,4191,670,4711,974,19321,716,123
-1-11-13-17-143-187-221-2,431-8,933-98,263-116,129-151,861-1,277,419-1,670,471-1,974,193-21,716,123

More Examples

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