Q: What are the factor combinations of the number 30,721,765?

 A:
Positive:   1 x 307217655 x 614435319 x 161693595 x 323387331 x 92815977 x 314451655 x 185634885 x 6289
Negative: -1 x -30721765-5 x -6144353-19 x -1616935-95 x -323387-331 x -92815-977 x -31445-1655 x -18563-4885 x -6289


How do I find the factor combinations of the number 30,721,765?

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 30,721,765, 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 30,721,765
-1 -30,721,765

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 30,721,765.

Example:
1 x 30,721,765 = 30,721,765
and
-1 x -30,721,765 = 30,721,765
Notice both answers equal 30,721,765

With that explanation out of the way, let's continue. Next, we take the number 30,721,765 and divide it by 2:

30,721,765 ÷ 2 = 15,360,882.5

If the quotient is a whole number, then 2 and 15,360,882.5 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 30,721,765
-1 -30,721,765

Now, we try dividing 30,721,765 by 3:

30,721,765 ÷ 3 = 10,240,588.3333

If the quotient is a whole number, then 3 and 10,240,588.3333 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 30,721,765
-1 -30,721,765

Let's try dividing by 4:

30,721,765 ÷ 4 = 7,680,441.25

If the quotient is a whole number, then 4 and 7,680,441.25 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 30,721,765
-1 30,721,765
Keep dividing by the next highest number until you cannot divide anymore.

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

1519953319771,6554,8856,28918,56331,44592,815323,3871,616,9356,144,35330,721,765
-1-5-19-95-331-977-1,655-4,885-6,289-18,563-31,445-92,815-323,387-1,616,935-6,144,353-30,721,765

More Examples

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