Q: What are the factor combinations of the number 235,807?

 A:
Positive:   1 x 23580711 x 2143713 x 1813917 x 1387197 x 2431143 x 1649187 x 1261221 x 1067
Negative: -1 x -235807-11 x -21437-13 x -18139-17 x -13871-97 x -2431-143 x -1649-187 x -1261-221 x -1067


How do I find the factor combinations of the number 235,807?

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 235,807, 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.

1 235,807
-1 -235,807

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 235,807.

Example:
1 x 235,807 = 235,807
and
-1 x -235,807 = 235,807
Notice both answers equal 235,807

With that explanation out of the way, let's continue. Next, we take the number 235,807 and divide it by 2:

235,807 ÷ 2 = 117,903.5

If the quotient is a whole number, then 2 and 117,903.5 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:

1 235,807
-1 -235,807

Now, we try dividing 235,807 by 3:

235,807 ÷ 3 = 78,602.3333

If the quotient is a whole number, then 3 and 78,602.3333 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:

1 235,807
-1 -235,807

Let's try dividing by 4:

235,807 ÷ 4 = 58,951.75

If the quotient is a whole number, then 4 and 58,951.75 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:

1 235,807
-1 235,807
Keep dividing by the next highest number until you cannot divide anymore.

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

1111317971431872211,0671,2611,6492,43113,87118,13921,437235,807
-1-11-13-17-97-143-187-221-1,067-1,261-1,649-2,431-13,871-18,139-21,437-235,807

More Examples

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