Q: What are the factor combinations of the number 48,209?

 A:
Positive:   1 x 482097 x 688771 x 67997 x 497
Negative: -1 x -48209-7 x -6887-71 x -679-97 x -497


How do I find the factor combinations of the number 48,209?

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 48,209, 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 48,209
-1 -48,209

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 48,209.

Example:
1 x 48,209 = 48,209
and
-1 x -48,209 = 48,209
Notice both answers equal 48,209

With that explanation out of the way, let's continue. Next, we take the number 48,209 and divide it by 2:

48,209 ÷ 2 = 24,104.5

If the quotient is a whole number, then 2 and 24,104.5 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 48,209
-1 -48,209

Now, we try dividing 48,209 by 3:

48,209 ÷ 3 = 16,069.6667

If the quotient is a whole number, then 3 and 16,069.6667 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 48,209
-1 -48,209

Let's try dividing by 4:

48,209 ÷ 4 = 12,052.25

If the quotient is a whole number, then 4 and 12,052.25 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 48,209
-1 48,209
Keep dividing by the next highest number until you cannot divide anymore.

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

1771974976796,88748,209
-1-7-71-97-497-679-6,887-48,209

More Examples

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