Q: What are the factor combinations of the number 467,915?

 A:
Positive:   1 x 4679155 x 935837 x 6684529 x 1613535 x 13369145 x 3227203 x 2305461 x 1015
Negative: -1 x -467915-5 x -93583-7 x -66845-29 x -16135-35 x -13369-145 x -3227-203 x -2305-461 x -1015


How do I find the factor combinations of the number 467,915?

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 467,915, 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.

1 467,915
-1 -467,915

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 467,915.

Example:
1 x 467,915 = 467,915
and
-1 x -467,915 = 467,915
Notice both answers equal 467,915

With that explanation out of the way, let's continue. Next, we take the number 467,915 and divide it by 2:

467,915 ÷ 2 = 233,957.5

If the quotient is a whole number, then 2 and 233,957.5 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:

1 467,915
-1 -467,915

Now, we try dividing 467,915 by 3:

467,915 ÷ 3 = 155,971.6667

If the quotient is a whole number, then 3 and 155,971.6667 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:

1 467,915
-1 -467,915

Let's try dividing by 4:

467,915 ÷ 4 = 116,978.75

If the quotient is a whole number, then 4 and 116,978.75 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:

1 467,915
-1 467,915
Keep dividing by the next highest number until you cannot divide anymore.

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

15729351452034611,0152,3053,22713,36916,13566,84593,583467,915
-1-5-7-29-35-145-203-461-1,015-2,305-3,227-13,369-16,135-66,845-93,583-467,915

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