Q: What are the factor combinations of the number 120,110,305?

 A:
Positive:   1 x 1201103055 x 240220617 x 1715861519 x 632159535 x 343172395 x 1264319133 x 903085665 x 180617
Negative: -1 x -120110305-5 x -24022061-7 x -17158615-19 x -6321595-35 x -3431723-95 x -1264319-133 x -903085-665 x -180617


How do I find the factor combinations of the number 120,110,305?

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 120,110,305, 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.

1 120,110,305
-1 -120,110,305

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 120,110,305.

Example:
1 x 120,110,305 = 120,110,305
and
-1 x -120,110,305 = 120,110,305
Notice both answers equal 120,110,305

With that explanation out of the way, let's continue. Next, we take the number 120,110,305 and divide it by 2:

120,110,305 ÷ 2 = 60,055,152.5

If the quotient is a whole number, then 2 and 60,055,152.5 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:

1 120,110,305
-1 -120,110,305

Now, we try dividing 120,110,305 by 3:

120,110,305 ÷ 3 = 40,036,768.3333

If the quotient is a whole number, then 3 and 40,036,768.3333 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:

1 120,110,305
-1 -120,110,305

Let's try dividing by 4:

120,110,305 ÷ 4 = 30,027,576.25

If the quotient is a whole number, then 4 and 30,027,576.25 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:

1 120,110,305
-1 120,110,305
Keep dividing by the next highest number until you cannot divide anymore.

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

157193595133665180,617903,0851,264,3193,431,7236,321,59517,158,61524,022,061120,110,305
-1-5-7-19-35-95-133-665-180,617-903,085-1,264,319-3,431,723-6,321,595-17,158,615-24,022,061-120,110,305

More Examples

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