Q: What are the factor combinations of the number 102,796?

 A:
Positive:   1 x 1027962 x 513984 x 2569931 x 331662 x 1658124 x 829
Negative: -1 x -102796-2 x -51398-4 x -25699-31 x -3316-62 x -1658-124 x -829


How do I find the factor combinations of the number 102,796?

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 102,796, 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.

1 102,796
-1 -102,796

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 102,796.

Example:
1 x 102,796 = 102,796
and
-1 x -102,796 = 102,796
Notice both answers equal 102,796

With that explanation out of the way, let's continue. Next, we take the number 102,796 and divide it by 2:

102,796 ÷ 2 = 51,398

If the quotient is a whole number, then 2 and 51,398 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 51,398 102,796
-1 -2 -51,398 -102,796

Now, we try dividing 102,796 by 3:

102,796 ÷ 3 = 34,265.3333

If the quotient is a whole number, then 3 and 34,265.3333 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 51,398 102,796
-1 -2 -51,398 -102,796

Let's try dividing by 4:

102,796 ÷ 4 = 25,699

If the quotient is a whole number, then 4 and 25,699 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 4 25,699 51,398 102,796
-1 -2 -4 -25,699 -51,398 102,796
Keep dividing by the next highest number until you cannot divide anymore.

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

12431621248291,6583,31625,69951,398102,796
-1-2-4-31-62-124-829-1,658-3,316-25,699-51,398-102,796

More Examples

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