Q: What are the factor combinations of the number 120,321,215?

 A:
Positive:   1 x 1203212155 x 240642437 x 1718874535 x 343774949 x 245553571 x 1694665245 x 491107355 x 338933497 x 2420952485 x 484193479 x 345856917 x 17395
Negative: -1 x -120321215-5 x -24064243-7 x -17188745-35 x -3437749-49 x -2455535-71 x -1694665-245 x -491107-355 x -338933-497 x -242095-2485 x -48419-3479 x -34585-6917 x -17395


How do I find the factor combinations of the number 120,321,215?

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 120,321,215, 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.

1 120,321,215
-1 -120,321,215

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 120,321,215.

Example:
1 x 120,321,215 = 120,321,215
and
-1 x -120,321,215 = 120,321,215
Notice both answers equal 120,321,215

With that explanation out of the way, let's continue. Next, we take the number 120,321,215 and divide it by 2:

120,321,215 ÷ 2 = 60,160,607.5

If the quotient is a whole number, then 2 and 60,160,607.5 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:

1 120,321,215
-1 -120,321,215

Now, we try dividing 120,321,215 by 3:

120,321,215 ÷ 3 = 40,107,071.6667

If the quotient is a whole number, then 3 and 40,107,071.6667 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:

1 120,321,215
-1 -120,321,215

Let's try dividing by 4:

120,321,215 ÷ 4 = 30,080,303.75

If the quotient is a whole number, then 4 and 30,080,303.75 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:

1 120,321,215
-1 120,321,215
Keep dividing by the next highest number until you cannot divide anymore.

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

1573549712453554972,4853,4796,91717,39534,58548,419242,095338,933491,1071,694,6652,455,5353,437,74917,188,74524,064,243120,321,215
-1-5-7-35-49-71-245-355-497-2,485-3,479-6,917-17,395-34,585-48,419-242,095-338,933-491,107-1,694,665-2,455,535-3,437,749-17,188,745-24,064,243-120,321,215

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