Q: What are the factor combinations of the number 23,456,719?

 A:
Positive:   1 x 2345671911 x 213242913 x 180436317 x 1379807143 x 164033187 x 125437221 x 1061392431 x 9649
Negative: -1 x -23456719-11 x -2132429-13 x -1804363-17 x -1379807-143 x -164033-187 x -125437-221 x -106139-2431 x -9649


How do I find the factor combinations of the number 23,456,719?

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 23,456,719, 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 23,456,719
-1 -23,456,719

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 23,456,719.

Example:
1 x 23,456,719 = 23,456,719
and
-1 x -23,456,719 = 23,456,719
Notice both answers equal 23,456,719

With that explanation out of the way, let's continue. Next, we take the number 23,456,719 and divide it by 2:

23,456,719 ÷ 2 = 11,728,359.5

If the quotient is a whole number, then 2 and 11,728,359.5 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 23,456,719
-1 -23,456,719

Now, we try dividing 23,456,719 by 3:

23,456,719 ÷ 3 = 7,818,906.3333

If the quotient is a whole number, then 3 and 7,818,906.3333 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 23,456,719
-1 -23,456,719

Let's try dividing by 4:

23,456,719 ÷ 4 = 5,864,179.75

If the quotient is a whole number, then 4 and 5,864,179.75 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 23,456,719
-1 23,456,719
Keep dividing by the next highest number until you cannot divide anymore.

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

11113171431872212,4319,649106,139125,437164,0331,379,8071,804,3632,132,42923,456,719
-1-11-13-17-143-187-221-2,431-9,649-106,139-125,437-164,033-1,379,807-1,804,363-2,132,429-23,456,719

More Examples

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