Q: What are the factor combinations of the number 273,325?

 A:
Positive:   1 x 2733255 x 5466513 x 2102525 x 1093329 x 942565 x 4205145 x 1885325 x 841377 x 725
Negative: -1 x -273325-5 x -54665-13 x -21025-25 x -10933-29 x -9425-65 x -4205-145 x -1885-325 x -841-377 x -725


How do I find the factor combinations of the number 273,325?

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 273,325, 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.

1 273,325
-1 -273,325

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 273,325.

Example:
1 x 273,325 = 273,325
and
-1 x -273,325 = 273,325
Notice both answers equal 273,325

With that explanation out of the way, let's continue. Next, we take the number 273,325 and divide it by 2:

273,325 ÷ 2 = 136,662.5

If the quotient is a whole number, then 2 and 136,662.5 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:

1 273,325
-1 -273,325

Now, we try dividing 273,325 by 3:

273,325 ÷ 3 = 91,108.3333

If the quotient is a whole number, then 3 and 91,108.3333 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:

1 273,325
-1 -273,325

Let's try dividing by 4:

273,325 ÷ 4 = 68,331.25

If the quotient is a whole number, then 4 and 68,331.25 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:

1 273,325
-1 273,325
Keep dividing by the next highest number until you cannot divide anymore.

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

15132529651453253777258411,8854,2059,42510,93321,02554,665273,325
-1-5-13-25-29-65-145-325-377-725-841-1,885-4,205-9,425-10,933-21,025-54,665-273,325

More Examples

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