Q: What are the factor combinations of the number 241,230,409?

 A:
Positive:   1 x 2412304097 x 3446148759 x 4088651359 x 671951413 x 5840931627 x 1482672513 x 9599311389 x 21181
Negative: -1 x -241230409-7 x -34461487-59 x -4088651-359 x -671951-413 x -584093-1627 x -148267-2513 x -95993-11389 x -21181


How do I find the factor combinations of the number 241,230,409?

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 241,230,409, 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.

1 241,230,409
-1 -241,230,409

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 241,230,409.

Example:
1 x 241,230,409 = 241,230,409
and
-1 x -241,230,409 = 241,230,409
Notice both answers equal 241,230,409

With that explanation out of the way, let's continue. Next, we take the number 241,230,409 and divide it by 2:

241,230,409 ÷ 2 = 120,615,204.5

If the quotient is a whole number, then 2 and 120,615,204.5 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:

1 241,230,409
-1 -241,230,409

Now, we try dividing 241,230,409 by 3:

241,230,409 ÷ 3 = 80,410,136.3333

If the quotient is a whole number, then 3 and 80,410,136.3333 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:

1 241,230,409
-1 -241,230,409

Let's try dividing by 4:

241,230,409 ÷ 4 = 60,307,602.25

If the quotient is a whole number, then 4 and 60,307,602.25 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:

1 241,230,409
-1 241,230,409
Keep dividing by the next highest number until you cannot divide anymore.

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

17593594131,6272,51311,38921,18195,993148,267584,093671,9514,088,65134,461,487241,230,409
-1-7-59-359-413-1,627-2,513-11,389-21,181-95,993-148,267-584,093-671,951-4,088,651-34,461,487-241,230,409

More Examples

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