Q: What are the factor combinations of the number 23,009,177?

 A:
Positive:   1 x 2300917717 x 135348123 x 100039983 x 277219391 x 58847709 x 324531411 x 163071909 x 12053
Negative: -1 x -23009177-17 x -1353481-23 x -1000399-83 x -277219-391 x -58847-709 x -32453-1411 x -16307-1909 x -12053


How do I find the factor combinations of the number 23,009,177?

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 23,009,177, 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 23,009,177
-1 -23,009,177

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 23,009,177.

Example:
1 x 23,009,177 = 23,009,177
and
-1 x -23,009,177 = 23,009,177
Notice both answers equal 23,009,177

With that explanation out of the way, let's continue. Next, we take the number 23,009,177 and divide it by 2:

23,009,177 ÷ 2 = 11,504,588.5

If the quotient is a whole number, then 2 and 11,504,588.5 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 23,009,177
-1 -23,009,177

Now, we try dividing 23,009,177 by 3:

23,009,177 ÷ 3 = 7,669,725.6667

If the quotient is a whole number, then 3 and 7,669,725.6667 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 23,009,177
-1 -23,009,177

Let's try dividing by 4:

23,009,177 ÷ 4 = 5,752,294.25

If the quotient is a whole number, then 4 and 5,752,294.25 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 23,009,177
-1 23,009,177
Keep dividing by the next highest number until you cannot divide anymore.

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

11723833917091,4111,90912,05316,30732,45358,847277,2191,000,3991,353,48123,009,177
-1-17-23-83-391-709-1,411-1,909-12,053-16,307-32,453-58,847-277,219-1,000,399-1,353,481-23,009,177

More Examples

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