Q: What are the factor combinations of the number 124,412,123?

 A:
Positive:   1 x 12441212311 x 1131019361 x 203954379 x 1574837671 x 185413869 x 1431672347 x 530094819 x 25817
Negative: -1 x -124412123-11 x -11310193-61 x -2039543-79 x -1574837-671 x -185413-869 x -143167-2347 x -53009-4819 x -25817


How do I find the factor combinations of the number 124,412,123?

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 124,412,123, 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.

1 124,412,123
-1 -124,412,123

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 124,412,123.

Example:
1 x 124,412,123 = 124,412,123
and
-1 x -124,412,123 = 124,412,123
Notice both answers equal 124,412,123

With that explanation out of the way, let's continue. Next, we take the number 124,412,123 and divide it by 2:

124,412,123 ÷ 2 = 62,206,061.5

If the quotient is a whole number, then 2 and 62,206,061.5 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:

1 124,412,123
-1 -124,412,123

Now, we try dividing 124,412,123 by 3:

124,412,123 ÷ 3 = 41,470,707.6667

If the quotient is a whole number, then 3 and 41,470,707.6667 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:

1 124,412,123
-1 -124,412,123

Let's try dividing by 4:

124,412,123 ÷ 4 = 31,103,030.75

If the quotient is a whole number, then 4 and 31,103,030.75 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:

1 124,412,123
-1 124,412,123
Keep dividing by the next highest number until you cannot divide anymore.

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

11161796718692,3474,81925,81753,009143,167185,4131,574,8372,039,54311,310,193124,412,123
-1-11-61-79-671-869-2,347-4,819-25,817-53,009-143,167-185,413-1,574,837-2,039,543-11,310,193-124,412,123

More Examples

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