Q: What are the factor combinations of the number 103,675?

 A:
Positive:   1 x 1036755 x 2073511 x 942513 x 797525 x 414729 x 357555 x 188565 x 1595143 x 725145 x 715275 x 377319 x 325
Negative: -1 x -103675-5 x -20735-11 x -9425-13 x -7975-25 x -4147-29 x -3575-55 x -1885-65 x -1595-143 x -725-145 x -715-275 x -377-319 x -325


How do I find the factor combinations of the number 103,675?

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 103,675, 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.

1 103,675
-1 -103,675

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 103,675.

Example:
1 x 103,675 = 103,675
and
-1 x -103,675 = 103,675
Notice both answers equal 103,675

With that explanation out of the way, let's continue. Next, we take the number 103,675 and divide it by 2:

103,675 ÷ 2 = 51,837.5

If the quotient is a whole number, then 2 and 51,837.5 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:

1 103,675
-1 -103,675

Now, we try dividing 103,675 by 3:

103,675 ÷ 3 = 34,558.3333

If the quotient is a whole number, then 3 and 34,558.3333 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:

1 103,675
-1 -103,675

Let's try dividing by 4:

103,675 ÷ 4 = 25,918.75

If the quotient is a whole number, then 4 and 25,918.75 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:

1 103,675
-1 103,675
Keep dividing by the next highest number until you cannot divide anymore.

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

151113252955651431452753193253777157251,5951,8853,5754,1477,9759,42520,735103,675
-1-5-11-13-25-29-55-65-143-145-275-319-325-377-715-725-1,595-1,885-3,575-4,147-7,975-9,425-20,735-103,675

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