Q: What are the factor combinations of the number 120,220,225?

 A:
Positive:   1 x 1202202255 x 2404404525 x 480880929 x 414552579 x 1521775145 x 829105395 x 304355725 x 1658211975 x 608712099 x 572752291 x 5247510495 x 11455
Negative: -1 x -120220225-5 x -24044045-25 x -4808809-29 x -4145525-79 x -1521775-145 x -829105-395 x -304355-725 x -165821-1975 x -60871-2099 x -57275-2291 x -52475-10495 x -11455


How do I find the factor combinations of the number 120,220,225?

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 120,220,225, 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.

1 120,220,225
-1 -120,220,225

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 120,220,225.

Example:
1 x 120,220,225 = 120,220,225
and
-1 x -120,220,225 = 120,220,225
Notice both answers equal 120,220,225

With that explanation out of the way, let's continue. Next, we take the number 120,220,225 and divide it by 2:

120,220,225 ÷ 2 = 60,110,112.5

If the quotient is a whole number, then 2 and 60,110,112.5 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:

1 120,220,225
-1 -120,220,225

Now, we try dividing 120,220,225 by 3:

120,220,225 ÷ 3 = 40,073,408.3333

If the quotient is a whole number, then 3 and 40,073,408.3333 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:

1 120,220,225
-1 -120,220,225

Let's try dividing by 4:

120,220,225 ÷ 4 = 30,055,056.25

If the quotient is a whole number, then 4 and 30,055,056.25 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:

1 120,220,225
-1 120,220,225
Keep dividing by the next highest number until you cannot divide anymore.

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

152529791453957251,9752,0992,29110,49511,45552,47557,27560,871165,821304,355829,1051,521,7754,145,5254,808,80924,044,045120,220,225
-1-5-25-29-79-145-395-725-1,975-2,099-2,291-10,495-11,455-52,475-57,275-60,871-165,821-304,355-829,105-1,521,775-4,145,525-4,808,809-24,044,045-120,220,225

More Examples

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