Q: What are the factor combinations of the number 120,610,219?

 A:
Positive:   1 x 12061021959 x 204424189 x 1355171103 x 1170973223 x 5408535251 x 229696077 x 198479167 x 13157
Negative: -1 x -120610219-59 x -2044241-89 x -1355171-103 x -1170973-223 x -540853-5251 x -22969-6077 x -19847-9167 x -13157


How do I find the factor combinations of the number 120,610,219?

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 120,610,219, 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.

1 120,610,219
-1 -120,610,219

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 120,610,219.

Example:
1 x 120,610,219 = 120,610,219
and
-1 x -120,610,219 = 120,610,219
Notice both answers equal 120,610,219

With that explanation out of the way, let's continue. Next, we take the number 120,610,219 and divide it by 2:

120,610,219 ÷ 2 = 60,305,109.5

If the quotient is a whole number, then 2 and 60,305,109.5 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:

1 120,610,219
-1 -120,610,219

Now, we try dividing 120,610,219 by 3:

120,610,219 ÷ 3 = 40,203,406.3333

If the quotient is a whole number, then 3 and 40,203,406.3333 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:

1 120,610,219
-1 -120,610,219

Let's try dividing by 4:

120,610,219 ÷ 4 = 30,152,554.75

If the quotient is a whole number, then 4 and 30,152,554.75 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:

1 120,610,219
-1 120,610,219
Keep dividing by the next highest number until you cannot divide anymore.

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

159891032235,2516,0779,16713,15719,84722,969540,8531,170,9731,355,1712,044,241120,610,219
-1-59-89-103-223-5,251-6,077-9,167-13,157-19,847-22,969-540,853-1,170,973-1,355,171-2,044,241-120,610,219

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