Q: What are the factor combinations of the number 427,823?

 A:
Positive:   1 x 42782311 x 3889319 x 2251723 x 1860189 x 4807209 x 2047253 x 1691437 x 979
Negative: -1 x -427823-11 x -38893-19 x -22517-23 x -18601-89 x -4807-209 x -2047-253 x -1691-437 x -979


How do I find the factor combinations of the number 427,823?

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 427,823, 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.

1 427,823
-1 -427,823

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 427,823.

Example:
1 x 427,823 = 427,823
and
-1 x -427,823 = 427,823
Notice both answers equal 427,823

With that explanation out of the way, let's continue. Next, we take the number 427,823 and divide it by 2:

427,823 ÷ 2 = 213,911.5

If the quotient is a whole number, then 2 and 213,911.5 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:

1 427,823
-1 -427,823

Now, we try dividing 427,823 by 3:

427,823 ÷ 3 = 142,607.6667

If the quotient is a whole number, then 3 and 142,607.6667 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:

1 427,823
-1 -427,823

Let's try dividing by 4:

427,823 ÷ 4 = 106,955.75

If the quotient is a whole number, then 4 and 106,955.75 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:

1 427,823
-1 427,823
Keep dividing by the next highest number until you cannot divide anymore.

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

1111923892092534379791,6912,0474,80718,60122,51738,893427,823
-1-11-19-23-89-209-253-437-979-1,691-2,047-4,807-18,601-22,517-38,893-427,823

More Examples

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