Q: What are the factor combinations of the number 612,827?

 A:
Positive:   1 x 61282741 x 14947
Negative: -1 x -612827-41 x -14947


How do I find the factor combinations of the number 612,827?

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 612,827, 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.

1 612,827
-1 -612,827

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 612,827.

Example:
1 x 612,827 = 612,827
and
-1 x -612,827 = 612,827
Notice both answers equal 612,827

With that explanation out of the way, let's continue. Next, we take the number 612,827 and divide it by 2:

612,827 ÷ 2 = 306,413.5

If the quotient is a whole number, then 2 and 306,413.5 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:

1 612,827
-1 -612,827

Now, we try dividing 612,827 by 3:

612,827 ÷ 3 = 204,275.6667

If the quotient is a whole number, then 3 and 204,275.6667 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:

1 612,827
-1 -612,827

Let's try dividing by 4:

612,827 ÷ 4 = 153,206.75

If the quotient is a whole number, then 4 and 153,206.75 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:

1 612,827
-1 612,827
Keep dividing by the next highest number until you cannot divide anymore.

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

14114,947612,827
-1-41-14,947-612,827

More Examples

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