Q: What are the factor combinations of the number 820,735,421?

 A:
Positive:   1 x 82073542111 x 74612311263 x 31206672893 x 283697
Negative: -1 x -820735421-11 x -74612311-263 x -3120667-2893 x -283697


How do I find the factor combinations of the number 820,735,421?

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 820,735,421, 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.

1 820,735,421
-1 -820,735,421

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 820,735,421.

Example:
1 x 820,735,421 = 820,735,421
and
-1 x -820,735,421 = 820,735,421
Notice both answers equal 820,735,421

With that explanation out of the way, let's continue. Next, we take the number 820,735,421 and divide it by 2:

820,735,421 ÷ 2 = 410,367,710.5

If the quotient is a whole number, then 2 and 410,367,710.5 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:

1 820,735,421
-1 -820,735,421

Now, we try dividing 820,735,421 by 3:

820,735,421 ÷ 3 = 273,578,473.6667

If the quotient is a whole number, then 3 and 273,578,473.6667 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:

1 820,735,421
-1 -820,735,421

Let's try dividing by 4:

820,735,421 ÷ 4 = 205,183,855.25

If the quotient is a whole number, then 4 and 205,183,855.25 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:

1 820,735,421
-1 820,735,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1112632,893283,6973,120,66774,612,311820,735,421
-1-11-263-2,893-283,697-3,120,667-74,612,311-820,735,421

More Examples

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