Q: What are the factor combinations of the number 120,102,367?

 A:
Positive:   1 x 1201023677 x 1715748111 x 1091839777 x 1559771967 x 1242011613 x 744596769 x 1774310637 x 11291
Negative: -1 x -120102367-7 x -17157481-11 x -10918397-77 x -1559771-967 x -124201-1613 x -74459-6769 x -17743-10637 x -11291


How do I find the factor combinations of the number 120,102,367?

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 120,102,367, 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.

1 120,102,367
-1 -120,102,367

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 120,102,367.

Example:
1 x 120,102,367 = 120,102,367
and
-1 x -120,102,367 = 120,102,367
Notice both answers equal 120,102,367

With that explanation out of the way, let's continue. Next, we take the number 120,102,367 and divide it by 2:

120,102,367 ÷ 2 = 60,051,183.5

If the quotient is a whole number, then 2 and 60,051,183.5 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:

1 120,102,367
-1 -120,102,367

Now, we try dividing 120,102,367 by 3:

120,102,367 ÷ 3 = 40,034,122.3333

If the quotient is a whole number, then 3 and 40,034,122.3333 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:

1 120,102,367
-1 -120,102,367

Let's try dividing by 4:

120,102,367 ÷ 4 = 30,025,591.75

If the quotient is a whole number, then 4 and 30,025,591.75 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:

1 120,102,367
-1 120,102,367
Keep dividing by the next highest number until you cannot divide anymore.

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

1711779671,6136,76910,63711,29117,74374,459124,2011,559,77110,918,39717,157,481120,102,367
-1-7-11-77-967-1,613-6,769-10,637-11,291-17,743-74,459-124,201-1,559,771-10,918,397-17,157,481-120,102,367

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