Q: What are the factor combinations of the number 243,815?

 A:
Positive:   1 x 2438155 x 4876311 x 2216513 x 1875531 x 786555 x 443365 x 3751121 x 2015143 x 1705155 x 1573341 x 715403 x 605
Negative: -1 x -243815-5 x -48763-11 x -22165-13 x -18755-31 x -7865-55 x -4433-65 x -3751-121 x -2015-143 x -1705-155 x -1573-341 x -715-403 x -605


How do I find the factor combinations of the number 243,815?

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 243,815, 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.

1 243,815
-1 -243,815

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 243,815.

Example:
1 x 243,815 = 243,815
and
-1 x -243,815 = 243,815
Notice both answers equal 243,815

With that explanation out of the way, let's continue. Next, we take the number 243,815 and divide it by 2:

243,815 ÷ 2 = 121,907.5

If the quotient is a whole number, then 2 and 121,907.5 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:

1 243,815
-1 -243,815

Now, we try dividing 243,815 by 3:

243,815 ÷ 3 = 81,271.6667

If the quotient is a whole number, then 3 and 81,271.6667 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:

1 243,815
-1 -243,815

Let's try dividing by 4:

243,815 ÷ 4 = 60,953.75

If the quotient is a whole number, then 4 and 60,953.75 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:

1 243,815
-1 243,815
Keep dividing by the next highest number until you cannot divide anymore.

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

1511133155651211431553414036057151,5731,7052,0153,7514,4337,86518,75522,16548,763243,815
-1-5-11-13-31-55-65-121-143-155-341-403-605-715-1,573-1,705-2,015-3,751-4,433-7,865-18,755-22,165-48,763-243,815

More Examples

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