Q: What are the factor combinations of the number 104,975?

 A:
Positive:   1 x 1049755 x 2099513 x 807517 x 617519 x 552525 x 419965 x 161585 x 123595 x 1105221 x 475247 x 425323 x 325
Negative: -1 x -104975-5 x -20995-13 x -8075-17 x -6175-19 x -5525-25 x -4199-65 x -1615-85 x -1235-95 x -1105-221 x -475-247 x -425-323 x -325


How do I find the factor combinations of the number 104,975?

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 104,975, 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.

1 104,975
-1 -104,975

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 104,975.

Example:
1 x 104,975 = 104,975
and
-1 x -104,975 = 104,975
Notice both answers equal 104,975

With that explanation out of the way, let's continue. Next, we take the number 104,975 and divide it by 2:

104,975 ÷ 2 = 52,487.5

If the quotient is a whole number, then 2 and 52,487.5 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:

1 104,975
-1 -104,975

Now, we try dividing 104,975 by 3:

104,975 ÷ 3 = 34,991.6667

If the quotient is a whole number, then 3 and 34,991.6667 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:

1 104,975
-1 -104,975

Let's try dividing by 4:

104,975 ÷ 4 = 26,243.75

If the quotient is a whole number, then 4 and 26,243.75 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:

1 104,975
-1 104,975
Keep dividing by the next highest number until you cannot divide anymore.

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

15131719256585952212473233254254751,1051,2351,6154,1995,5256,1758,07520,995104,975
-1-5-13-17-19-25-65-85-95-221-247-323-325-425-475-1,105-1,235-1,615-4,199-5,525-6,175-8,075-20,995-104,975

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