Q: What are the factor combinations of the number 10,375?

 A:
Positive:   1 x 103755 x 207525 x 41583 x 125
Negative: -1 x -10375-5 x -2075-25 x -415-83 x -125


How do I find the factor combinations of the number 10,375?

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 10,375, 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 10,375
-1 -10,375

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 10,375.

Example:
1 x 10,375 = 10,375
and
-1 x -10,375 = 10,375
Notice both answers equal 10,375

With that explanation out of the way, let's continue. Next, we take the number 10,375 and divide it by 2:

10,375 ÷ 2 = 5,187.5

If the quotient is a whole number, then 2 and 5,187.5 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 10,375
-1 -10,375

Now, we try dividing 10,375 by 3:

10,375 ÷ 3 = 3,458.3333

If the quotient is a whole number, then 3 and 3,458.3333 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 10,375
-1 -10,375

Let's try dividing by 4:

10,375 ÷ 4 = 2,593.75

If the quotient is a whole number, then 4 and 2,593.75 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 10,375
-1 10,375
Keep dividing by the next highest number until you cannot divide anymore.

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

1525831254152,07510,375
-1-5-25-83-125-415-2,075-10,375

More Examples

Here are some more numbers to try:

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