Q: What are the factor combinations of the number 617,937?

 A:
Positive:   1 x 6179373 x 20597919 x 3252337 x 1670157 x 10841111 x 5567293 x 2109703 x 879
Negative: -1 x -617937-3 x -205979-19 x -32523-37 x -16701-57 x -10841-111 x -5567-293 x -2109-703 x -879


How do I find the factor combinations of the number 617,937?

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 617,937, 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.

1 617,937
-1 -617,937

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 617,937.

Example:
1 x 617,937 = 617,937
and
-1 x -617,937 = 617,937
Notice both answers equal 617,937

With that explanation out of the way, let's continue. Next, we take the number 617,937 and divide it by 2:

617,937 ÷ 2 = 308,968.5

If the quotient is a whole number, then 2 and 308,968.5 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:

1 617,937
-1 -617,937

Now, we try dividing 617,937 by 3:

617,937 ÷ 3 = 205,979

If the quotient is a whole number, then 3 and 205,979 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 205,979 617,937
-1 -3 -205,979 -617,937

Let's try dividing by 4:

617,937 ÷ 4 = 154,484.25

If the quotient is a whole number, then 4 and 154,484.25 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 3 205,979 617,937
-1 -3 -205,979 617,937
Keep dividing by the next highest number until you cannot divide anymore.

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

131937571112937038792,1095,56710,84116,70132,523205,979617,937
-1-3-19-37-57-111-293-703-879-2,109-5,567-10,841-16,701-32,523-205,979-617,937

More Examples

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