Q: What are the factor combinations of the number 54,703?

 A:
Positive:   1 x 5470311 x 4973
Negative: -1 x -54703-11 x -4973


How do I find the factor combinations of the number 54,703?

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 54,703, 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 54,703
-1 -54,703

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 54,703.

Example:
1 x 54,703 = 54,703
and
-1 x -54,703 = 54,703
Notice both answers equal 54,703

With that explanation out of the way, let's continue. Next, we take the number 54,703 and divide it by 2:

54,703 ÷ 2 = 27,351.5

If the quotient is a whole number, then 2 and 27,351.5 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 54,703
-1 -54,703

Now, we try dividing 54,703 by 3:

54,703 ÷ 3 = 18,234.3333

If the quotient is a whole number, then 3 and 18,234.3333 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 54,703
-1 -54,703

Let's try dividing by 4:

54,703 ÷ 4 = 13,675.75

If the quotient is a whole number, then 4 and 13,675.75 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 54,703
-1 54,703
Keep dividing by the next highest number until you cannot divide anymore.

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

1114,97354,703
-1-11-4,973-54,703

More Examples

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