Q: What are the factor combinations of the number 694,734?

 A:
Positive:   1 x 6947342 x 3473673 x 2315786 x 11578989 x 7806178 x 3903267 x 2602534 x 1301
Negative: -1 x -694734-2 x -347367-3 x -231578-6 x -115789-89 x -7806-178 x -3903-267 x -2602-534 x -1301


How do I find the factor combinations of the number 694,734?

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 694,734, 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.

1 694,734
-1 -694,734

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 694,734.

Example:
1 x 694,734 = 694,734
and
-1 x -694,734 = 694,734
Notice both answers equal 694,734

With that explanation out of the way, let's continue. Next, we take the number 694,734 and divide it by 2:

694,734 ÷ 2 = 347,367

If the quotient is a whole number, then 2 and 347,367 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 2 347,367 694,734
-1 -2 -347,367 -694,734

Now, we try dividing 694,734 by 3:

694,734 ÷ 3 = 231,578

If the quotient is a whole number, then 3 and 231,578 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 2 3 231,578 347,367 694,734
-1 -2 -3 -231,578 -347,367 -694,734

Let's try dividing by 4:

694,734 ÷ 4 = 173,683.5

If the quotient is a whole number, then 4 and 173,683.5 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 2 3 231,578 347,367 694,734
-1 -2 -3 -231,578 -347,367 694,734
Keep dividing by the next highest number until you cannot divide anymore.

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

1236891782675341,3012,6023,9037,806115,789231,578347,367694,734
-1-2-3-6-89-178-267-534-1,301-2,602-3,903-7,806-115,789-231,578-347,367-694,734

More Examples

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