Q: What are the factor combinations of the number 227,503?

 A:
Positive:   1 x 22750383 x 2741
Negative: -1 x -227503-83 x -2741


How do I find the factor combinations of the number 227,503?

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 227,503, 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.

1 227,503
-1 -227,503

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 227,503.

Example:
1 x 227,503 = 227,503
and
-1 x -227,503 = 227,503
Notice both answers equal 227,503

With that explanation out of the way, let's continue. Next, we take the number 227,503 and divide it by 2:

227,503 ÷ 2 = 113,751.5

If the quotient is a whole number, then 2 and 113,751.5 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:

1 227,503
-1 -227,503

Now, we try dividing 227,503 by 3:

227,503 ÷ 3 = 75,834.3333

If the quotient is a whole number, then 3 and 75,834.3333 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:

1 227,503
-1 -227,503

Let's try dividing by 4:

227,503 ÷ 4 = 56,875.75

If the quotient is a whole number, then 4 and 56,875.75 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:

1 227,503
-1 227,503
Keep dividing by the next highest number until you cannot divide anymore.

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

1832,741227,503
-1-83-2,741-227,503

More Examples

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