Q: What are the factor combinations of the number 121,840,241?

 A:
Positive:   1 x 12184024117 x 716707361 x 1997381293 x 415837401 x 3038411037 x 1174934981 x 244616817 x 17873
Negative: -1 x -121840241-17 x -7167073-61 x -1997381-293 x -415837-401 x -303841-1037 x -117493-4981 x -24461-6817 x -17873


How do I find the factor combinations of the number 121,840,241?

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 121,840,241, 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.

1 121,840,241
-1 -121,840,241

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 121,840,241.

Example:
1 x 121,840,241 = 121,840,241
and
-1 x -121,840,241 = 121,840,241
Notice both answers equal 121,840,241

With that explanation out of the way, let's continue. Next, we take the number 121,840,241 and divide it by 2:

121,840,241 ÷ 2 = 60,920,120.5

If the quotient is a whole number, then 2 and 60,920,120.5 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:

1 121,840,241
-1 -121,840,241

Now, we try dividing 121,840,241 by 3:

121,840,241 ÷ 3 = 40,613,413.6667

If the quotient is a whole number, then 3 and 40,613,413.6667 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:

1 121,840,241
-1 -121,840,241

Let's try dividing by 4:

121,840,241 ÷ 4 = 30,460,060.25

If the quotient is a whole number, then 4 and 30,460,060.25 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:

1 121,840,241
-1 121,840,241
Keep dividing by the next highest number until you cannot divide anymore.

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

117612934011,0374,9816,81717,87324,461117,493303,841415,8371,997,3817,167,073121,840,241
-1-17-61-293-401-1,037-4,981-6,817-17,873-24,461-117,493-303,841-415,837-1,997,381-7,167,073-121,840,241

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