Q: What are the factor combinations of the number 123,845?

 A:
Positive:   1 x 1238455 x 2476917 x 728531 x 399547 x 263585 x 1457155 x 799235 x 527
Negative: -1 x -123845-5 x -24769-17 x -7285-31 x -3995-47 x -2635-85 x -1457-155 x -799-235 x -527


How do I find the factor combinations of the number 123,845?

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 123,845, 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.

1 123,845
-1 -123,845

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 123,845.

Example:
1 x 123,845 = 123,845
and
-1 x -123,845 = 123,845
Notice both answers equal 123,845

With that explanation out of the way, let's continue. Next, we take the number 123,845 and divide it by 2:

123,845 ÷ 2 = 61,922.5

If the quotient is a whole number, then 2 and 61,922.5 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:

1 123,845
-1 -123,845

Now, we try dividing 123,845 by 3:

123,845 ÷ 3 = 41,281.6667

If the quotient is a whole number, then 3 and 41,281.6667 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:

1 123,845
-1 -123,845

Let's try dividing by 4:

123,845 ÷ 4 = 30,961.25

If the quotient is a whole number, then 4 and 30,961.25 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:

1 123,845
-1 123,845
Keep dividing by the next highest number until you cannot divide anymore.

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

15173147851552355277991,4572,6353,9957,28524,769123,845
-1-5-17-31-47-85-155-235-527-799-1,457-2,635-3,995-7,285-24,769-123,845

More Examples

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