Q: What are the factor combinations of the number 110,825?

 A:
Positive:   1 x 1108255 x 2216511 x 1007513 x 852525 x 443331 x 357555 x 201565 x 1705143 x 775155 x 715275 x 403325 x 341
Negative: -1 x -110825-5 x -22165-11 x -10075-13 x -8525-25 x -4433-31 x -3575-55 x -2015-65 x -1705-143 x -775-155 x -715-275 x -403-325 x -341


How do I find the factor combinations of the number 110,825?

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 110,825, 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.

1 110,825
-1 -110,825

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 110,825.

Example:
1 x 110,825 = 110,825
and
-1 x -110,825 = 110,825
Notice both answers equal 110,825

With that explanation out of the way, let's continue. Next, we take the number 110,825 and divide it by 2:

110,825 ÷ 2 = 55,412.5

If the quotient is a whole number, then 2 and 55,412.5 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:

1 110,825
-1 -110,825

Now, we try dividing 110,825 by 3:

110,825 ÷ 3 = 36,941.6667

If the quotient is a whole number, then 3 and 36,941.6667 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:

1 110,825
-1 -110,825

Let's try dividing by 4:

110,825 ÷ 4 = 27,706.25

If the quotient is a whole number, then 4 and 27,706.25 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:

1 110,825
-1 110,825
Keep dividing by the next highest number until you cannot divide anymore.

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

151113253155651431552753253414037157751,7052,0153,5754,4338,52510,07522,165110,825
-1-5-11-13-25-31-55-65-143-155-275-325-341-403-715-775-1,705-2,015-3,575-4,433-8,525-10,075-22,165-110,825

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