Q: What are the factor combinations of the number 120,401,045?

 A:
Positive:   1 x 1204010455 x 2408020983 x 1450615223 x 539915415 x 2901231115 x 1079831301 x 925456505 x 18509
Negative: -1 x -120401045-5 x -24080209-83 x -1450615-223 x -539915-415 x -290123-1115 x -107983-1301 x -92545-6505 x -18509


How do I find the factor combinations of the number 120,401,045?

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 120,401,045, 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.

1 120,401,045
-1 -120,401,045

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 120,401,045.

Example:
1 x 120,401,045 = 120,401,045
and
-1 x -120,401,045 = 120,401,045
Notice both answers equal 120,401,045

With that explanation out of the way, let's continue. Next, we take the number 120,401,045 and divide it by 2:

120,401,045 ÷ 2 = 60,200,522.5

If the quotient is a whole number, then 2 and 60,200,522.5 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:

1 120,401,045
-1 -120,401,045

Now, we try dividing 120,401,045 by 3:

120,401,045 ÷ 3 = 40,133,681.6667

If the quotient is a whole number, then 3 and 40,133,681.6667 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:

1 120,401,045
-1 -120,401,045

Let's try dividing by 4:

120,401,045 ÷ 4 = 30,100,261.25

If the quotient is a whole number, then 4 and 30,100,261.25 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:

1 120,401,045
-1 120,401,045
Keep dividing by the next highest number until you cannot divide anymore.

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

15832234151,1151,3016,50518,50992,545107,983290,123539,9151,450,61524,080,209120,401,045
-1-5-83-223-415-1,115-1,301-6,505-18,509-92,545-107,983-290,123-539,915-1,450,615-24,080,209-120,401,045

More Examples

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