Q: What are the factor combinations of the number 242,305?

 A:
Positive:   1 x 2423055 x 484617 x 3461523 x 1053535 x 692343 x 563549 x 4945115 x 2107161 x 1505215 x 1127245 x 989301 x 805
Negative: -1 x -242305-5 x -48461-7 x -34615-23 x -10535-35 x -6923-43 x -5635-49 x -4945-115 x -2107-161 x -1505-215 x -1127-245 x -989-301 x -805


How do I find the factor combinations of the number 242,305?

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 242,305, 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.

1 242,305
-1 -242,305

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 242,305.

Example:
1 x 242,305 = 242,305
and
-1 x -242,305 = 242,305
Notice both answers equal 242,305

With that explanation out of the way, let's continue. Next, we take the number 242,305 and divide it by 2:

242,305 ÷ 2 = 121,152.5

If the quotient is a whole number, then 2 and 121,152.5 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:

1 242,305
-1 -242,305

Now, we try dividing 242,305 by 3:

242,305 ÷ 3 = 80,768.3333

If the quotient is a whole number, then 3 and 80,768.3333 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:

1 242,305
-1 -242,305

Let's try dividing by 4:

242,305 ÷ 4 = 60,576.25

If the quotient is a whole number, then 4 and 60,576.25 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:

1 242,305
-1 242,305
Keep dividing by the next highest number until you cannot divide anymore.

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

157233543491151612152453018059891,1271,5052,1074,9455,6356,92310,53534,61548,461242,305
-1-5-7-23-35-43-49-115-161-215-245-301-805-989-1,127-1,505-2,107-4,945-5,635-6,923-10,535-34,615-48,461-242,305

More Examples

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