Q: What are the factor combinations of the number 696,815?

 A:
Positive:   1 x 6968155 x 1393637 x 9954535 x 1990943 x 16205215 x 3241301 x 2315463 x 1505
Negative: -1 x -696815-5 x -139363-7 x -99545-35 x -19909-43 x -16205-215 x -3241-301 x -2315-463 x -1505


How do I find the factor combinations of the number 696,815?

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 696,815, 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.

1 696,815
-1 -696,815

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 696,815.

Example:
1 x 696,815 = 696,815
and
-1 x -696,815 = 696,815
Notice both answers equal 696,815

With that explanation out of the way, let's continue. Next, we take the number 696,815 and divide it by 2:

696,815 ÷ 2 = 348,407.5

If the quotient is a whole number, then 2 and 348,407.5 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:

1 696,815
-1 -696,815

Now, we try dividing 696,815 by 3:

696,815 ÷ 3 = 232,271.6667

If the quotient is a whole number, then 3 and 232,271.6667 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:

1 696,815
-1 -696,815

Let's try dividing by 4:

696,815 ÷ 4 = 174,203.75

If the quotient is a whole number, then 4 and 174,203.75 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:

1 696,815
-1 696,815
Keep dividing by the next highest number until you cannot divide anymore.

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

15735432153014631,5052,3153,24116,20519,90999,545139,363696,815
-1-5-7-35-43-215-301-463-1,505-2,315-3,241-16,205-19,909-99,545-139,363-696,815

More Examples

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