Q: What are the factor combinations of the number 241,322,321?

 A:
Positive:   1 x 24132232131 x 778459143 x 5612147269 x 897109673 x 3585771333 x 1810378339 x 2893911567 x 20863
Negative: -1 x -241322321-31 x -7784591-43 x -5612147-269 x -897109-673 x -358577-1333 x -181037-8339 x -28939-11567 x -20863


How do I find the factor combinations of the number 241,322,321?

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 241,322,321, 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.

1 241,322,321
-1 -241,322,321

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 241,322,321.

Example:
1 x 241,322,321 = 241,322,321
and
-1 x -241,322,321 = 241,322,321
Notice both answers equal 241,322,321

With that explanation out of the way, let's continue. Next, we take the number 241,322,321 and divide it by 2:

241,322,321 ÷ 2 = 120,661,160.5

If the quotient is a whole number, then 2 and 120,661,160.5 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:

1 241,322,321
-1 -241,322,321

Now, we try dividing 241,322,321 by 3:

241,322,321 ÷ 3 = 80,440,773.6667

If the quotient is a whole number, then 3 and 80,440,773.6667 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:

1 241,322,321
-1 -241,322,321

Let's try dividing by 4:

241,322,321 ÷ 4 = 60,330,580.25

If the quotient is a whole number, then 4 and 60,330,580.25 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:

1 241,322,321
-1 241,322,321
Keep dividing by the next highest number until you cannot divide anymore.

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

131432696731,3338,33911,56720,86328,939181,037358,577897,1095,612,1477,784,591241,322,321
-1-31-43-269-673-1,333-8,339-11,567-20,863-28,939-181,037-358,577-897,109-5,612,147-7,784,591-241,322,321

More Examples

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