Q: What are the factor combinations of the number 437,503?

 A:
Positive:   1 x 43750311 x 3977331 x 14113341 x 1283
Negative: -1 x -437503-11 x -39773-31 x -14113-341 x -1283


How do I find the factor combinations of the number 437,503?

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 437,503, 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.

1 437,503
-1 -437,503

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 437,503.

Example:
1 x 437,503 = 437,503
and
-1 x -437,503 = 437,503
Notice both answers equal 437,503

With that explanation out of the way, let's continue. Next, we take the number 437,503 and divide it by 2:

437,503 ÷ 2 = 218,751.5

If the quotient is a whole number, then 2 and 218,751.5 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:

1 437,503
-1 -437,503

Now, we try dividing 437,503 by 3:

437,503 ÷ 3 = 145,834.3333

If the quotient is a whole number, then 3 and 145,834.3333 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:

1 437,503
-1 -437,503

Let's try dividing by 4:

437,503 ÷ 4 = 109,375.75

If the quotient is a whole number, then 4 and 109,375.75 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:

1 437,503
-1 437,503
Keep dividing by the next highest number until you cannot divide anymore.

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

111313411,28314,11339,773437,503
-1-11-31-341-1,283-14,113-39,773-437,503

More Examples

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