Q: What are the factor combinations of the number 123,304,015?

 A:
Positive:   1 x 1233040155 x 2466080319 x 648968541 x 300741595 x 1297937205 x 601483779 x 1582853895 x 31657
Negative: -1 x -123304015-5 x -24660803-19 x -6489685-41 x -3007415-95 x -1297937-205 x -601483-779 x -158285-3895 x -31657


How do I find the factor combinations of the number 123,304,015?

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 123,304,015, 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.

1 123,304,015
-1 -123,304,015

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 123,304,015.

Example:
1 x 123,304,015 = 123,304,015
and
-1 x -123,304,015 = 123,304,015
Notice both answers equal 123,304,015

With that explanation out of the way, let's continue. Next, we take the number 123,304,015 and divide it by 2:

123,304,015 ÷ 2 = 61,652,007.5

If the quotient is a whole number, then 2 and 61,652,007.5 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:

1 123,304,015
-1 -123,304,015

Now, we try dividing 123,304,015 by 3:

123,304,015 ÷ 3 = 41,101,338.3333

If the quotient is a whole number, then 3 and 41,101,338.3333 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:

1 123,304,015
-1 -123,304,015

Let's try dividing by 4:

123,304,015 ÷ 4 = 30,826,003.75

If the quotient is a whole number, then 4 and 30,826,003.75 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:

1 123,304,015
-1 123,304,015
Keep dividing by the next highest number until you cannot divide anymore.

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

151941952057793,89531,657158,285601,4831,297,9373,007,4156,489,68524,660,803123,304,015
-1-5-19-41-95-205-779-3,895-31,657-158,285-601,483-1,297,937-3,007,415-6,489,685-24,660,803-123,304,015

More Examples

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