Q: What are the factor combinations of the number 23,404,409?

 A:
Positive:   1 x 234044097 x 334348719 x 123181123 x 101758349 x 477641133 x 175973161 x 145369437 x 53557931 x 251391093 x 214131127 x 207673059 x 7651
Negative: -1 x -23404409-7 x -3343487-19 x -1231811-23 x -1017583-49 x -477641-133 x -175973-161 x -145369-437 x -53557-931 x -25139-1093 x -21413-1127 x -20767-3059 x -7651


How do I find the factor combinations of the number 23,404,409?

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 23,404,409, 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 23,404,409
-1 -23,404,409

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 23,404,409.

Example:
1 x 23,404,409 = 23,404,409
and
-1 x -23,404,409 = 23,404,409
Notice both answers equal 23,404,409

With that explanation out of the way, let's continue. Next, we take the number 23,404,409 and divide it by 2:

23,404,409 ÷ 2 = 11,702,204.5

If the quotient is a whole number, then 2 and 11,702,204.5 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 23,404,409
-1 -23,404,409

Now, we try dividing 23,404,409 by 3:

23,404,409 ÷ 3 = 7,801,469.6667

If the quotient is a whole number, then 3 and 7,801,469.6667 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 23,404,409
-1 -23,404,409

Let's try dividing by 4:

23,404,409 ÷ 4 = 5,851,102.25

If the quotient is a whole number, then 4 and 5,851,102.25 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 23,404,409
-1 23,404,409
Keep dividing by the next highest number until you cannot divide anymore.

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

171923491331614379311,0931,1273,0597,65120,76721,41325,13953,557145,369175,973477,6411,017,5831,231,8113,343,48723,404,409
-1-7-19-23-49-133-161-437-931-1,093-1,127-3,059-7,651-20,767-21,413-25,139-53,557-145,369-175,973-477,641-1,017,583-1,231,811-3,343,487-23,404,409

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