Q: What are the factor combinations of the number 253,825?

 A:
Positive:   1 x 2538255 x 5076511 x 2307513 x 1952525 x 1015355 x 461565 x 390571 x 3575143 x 1775275 x 923325 x 781355 x 715
Negative: -1 x -253825-5 x -50765-11 x -23075-13 x -19525-25 x -10153-55 x -4615-65 x -3905-71 x -3575-143 x -1775-275 x -923-325 x -781-355 x -715


How do I find the factor combinations of the number 253,825?

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 253,825, 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.

1 253,825
-1 -253,825

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 253,825.

Example:
1 x 253,825 = 253,825
and
-1 x -253,825 = 253,825
Notice both answers equal 253,825

With that explanation out of the way, let's continue. Next, we take the number 253,825 and divide it by 2:

253,825 ÷ 2 = 126,912.5

If the quotient is a whole number, then 2 and 126,912.5 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:

1 253,825
-1 -253,825

Now, we try dividing 253,825 by 3:

253,825 ÷ 3 = 84,608.3333

If the quotient is a whole number, then 3 and 84,608.3333 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:

1 253,825
-1 -253,825

Let's try dividing by 4:

253,825 ÷ 4 = 63,456.25

If the quotient is a whole number, then 4 and 63,456.25 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:

1 253,825
-1 253,825
Keep dividing by the next highest number until you cannot divide anymore.

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

151113255565711432753253557157819231,7753,5753,9054,61510,15319,52523,07550,765253,825
-1-5-11-13-25-55-65-71-143-275-325-355-715-781-923-1,775-3,575-3,905-4,615-10,153-19,525-23,075-50,765-253,825

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