Q: What are the factor combinations of the number 120,535,321?

 A:
Positive:   1 x 12053532117 x 709031343 x 2803147181 x 665941731 x 164891911 x 1323113077 x 391737783 x 15487
Negative: -1 x -120535321-17 x -7090313-43 x -2803147-181 x -665941-731 x -164891-911 x -132311-3077 x -39173-7783 x -15487


How do I find the factor combinations of the number 120,535,321?

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 120,535,321, 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.

1 120,535,321
-1 -120,535,321

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 120,535,321.

Example:
1 x 120,535,321 = 120,535,321
and
-1 x -120,535,321 = 120,535,321
Notice both answers equal 120,535,321

With that explanation out of the way, let's continue. Next, we take the number 120,535,321 and divide it by 2:

120,535,321 ÷ 2 = 60,267,660.5

If the quotient is a whole number, then 2 and 60,267,660.5 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:

1 120,535,321
-1 -120,535,321

Now, we try dividing 120,535,321 by 3:

120,535,321 ÷ 3 = 40,178,440.3333

If the quotient is a whole number, then 3 and 40,178,440.3333 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:

1 120,535,321
-1 -120,535,321

Let's try dividing by 4:

120,535,321 ÷ 4 = 30,133,830.25

If the quotient is a whole number, then 4 and 30,133,830.25 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:

1 120,535,321
-1 120,535,321
Keep dividing by the next highest number until you cannot divide anymore.

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

117431817319113,0777,78315,48739,173132,311164,891665,9412,803,1477,090,313120,535,321
-1-17-43-181-731-911-3,077-7,783-15,487-39,173-132,311-164,891-665,941-2,803,147-7,090,313-120,535,321

More Examples

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