Q: What are the factor combinations of the number 320,411?

 A:
Positive:   1 x 3204117 x 4577313 x 2464749 x 653991 x 3521503 x 637
Negative: -1 x -320411-7 x -45773-13 x -24647-49 x -6539-91 x -3521-503 x -637


How do I find the factor combinations of the number 320,411?

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 320,411, 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.

1 320,411
-1 -320,411

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 320,411.

Example:
1 x 320,411 = 320,411
and
-1 x -320,411 = 320,411
Notice both answers equal 320,411

With that explanation out of the way, let's continue. Next, we take the number 320,411 and divide it by 2:

320,411 ÷ 2 = 160,205.5

If the quotient is a whole number, then 2 and 160,205.5 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:

1 320,411
-1 -320,411

Now, we try dividing 320,411 by 3:

320,411 ÷ 3 = 106,803.6667

If the quotient is a whole number, then 3 and 106,803.6667 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:

1 320,411
-1 -320,411

Let's try dividing by 4:

320,411 ÷ 4 = 80,102.75

If the quotient is a whole number, then 4 and 80,102.75 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:

1 320,411
-1 320,411
Keep dividing by the next highest number until you cannot divide anymore.

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

171349915036373,5216,53924,64745,773320,411
-1-7-13-49-91-503-637-3,521-6,539-24,647-45,773-320,411

More Examples

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