Q: What are the factor combinations of the number 1,683,598?

 A:
Positive:   1 x 16835982 x 8417997 x 24051414 x 12025753 x 31766106 x 15883371 x 4538742 x 2269
Negative: -1 x -1683598-2 x -841799-7 x -240514-14 x -120257-53 x -31766-106 x -15883-371 x -4538-742 x -2269


How do I find the factor combinations of the number 1,683,598?

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 1,683,598, 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 1,683,598
-1 -1,683,598

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 1,683,598.

Example:
1 x 1,683,598 = 1,683,598
and
-1 x -1,683,598 = 1,683,598
Notice both answers equal 1,683,598

With that explanation out of the way, let's continue. Next, we take the number 1,683,598 and divide it by 2:

1,683,598 ÷ 2 = 841,799

If the quotient is a whole number, then 2 and 841,799 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 2 841,799 1,683,598
-1 -2 -841,799 -1,683,598

Now, we try dividing 1,683,598 by 3:

1,683,598 ÷ 3 = 561,199.3333

If the quotient is a whole number, then 3 and 561,199.3333 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 2 841,799 1,683,598
-1 -2 -841,799 -1,683,598

Let's try dividing by 4:

1,683,598 ÷ 4 = 420,899.5

If the quotient is a whole number, then 4 and 420,899.5 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 2 841,799 1,683,598
-1 -2 -841,799 1,683,598
Keep dividing by the next highest number until you cannot divide anymore.

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

12714531063717422,2694,53815,88331,766120,257240,514841,7991,683,598
-1-2-7-14-53-106-371-742-2,269-4,538-15,883-31,766-120,257-240,514-841,799-1,683,598

More Examples

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