Q: What are the factor combinations of the number 23,240,329?

 A:
Positive:   1 x 232403297 x 332004737 x 62811761 x 380989259 x 89731427 x 544271471 x 157992257 x 10297
Negative: -1 x -23240329-7 x -3320047-37 x -628117-61 x -380989-259 x -89731-427 x -54427-1471 x -15799-2257 x -10297


How do I find the factor combinations of the number 23,240,329?

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 23,240,329, 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 23,240,329
-1 -23,240,329

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 23,240,329.

Example:
1 x 23,240,329 = 23,240,329
and
-1 x -23,240,329 = 23,240,329
Notice both answers equal 23,240,329

With that explanation out of the way, let's continue. Next, we take the number 23,240,329 and divide it by 2:

23,240,329 ÷ 2 = 11,620,164.5

If the quotient is a whole number, then 2 and 11,620,164.5 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 23,240,329
-1 -23,240,329

Now, we try dividing 23,240,329 by 3:

23,240,329 ÷ 3 = 7,746,776.3333

If the quotient is a whole number, then 3 and 7,746,776.3333 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 23,240,329
-1 -23,240,329

Let's try dividing by 4:

23,240,329 ÷ 4 = 5,810,082.25

If the quotient is a whole number, then 4 and 5,810,082.25 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 23,240,329
-1 23,240,329
Keep dividing by the next highest number until you cannot divide anymore.

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

1737612594271,4712,25710,29715,79954,42789,731380,989628,1173,320,04723,240,329
-1-7-37-61-259-427-1,471-2,257-10,297-15,799-54,427-89,731-380,989-628,117-3,320,047-23,240,329

More Examples

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