Q: What are the factor combinations of the number 122,945?

 A:
Positive:   1 x 1229455 x 2458967 x 1835335 x 367
Negative: -1 x -122945-5 x -24589-67 x -1835-335 x -367


How do I find the factor combinations of the number 122,945?

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 122,945, 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.

1 122,945
-1 -122,945

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 122,945.

Example:
1 x 122,945 = 122,945
and
-1 x -122,945 = 122,945
Notice both answers equal 122,945

With that explanation out of the way, let's continue. Next, we take the number 122,945 and divide it by 2:

122,945 ÷ 2 = 61,472.5

If the quotient is a whole number, then 2 and 61,472.5 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:

1 122,945
-1 -122,945

Now, we try dividing 122,945 by 3:

122,945 ÷ 3 = 40,981.6667

If the quotient is a whole number, then 3 and 40,981.6667 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:

1 122,945
-1 -122,945

Let's try dividing by 4:

122,945 ÷ 4 = 30,736.25

If the quotient is a whole number, then 4 and 30,736.25 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:

1 122,945
-1 122,945
Keep dividing by the next highest number until you cannot divide anymore.

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

15673353671,83524,589122,945
-1-5-67-335-367-1,835-24,589-122,945

More Examples

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