Q: What are the factor combinations of the number 360,362,311?

 A:
Positive:   1 x 36036231117 x 21197783113 x 3189047149 x 24185391259 x 2862291921 x 1875912533 x 14226716837 x 21403
Negative: -1 x -360362311-17 x -21197783-113 x -3189047-149 x -2418539-1259 x -286229-1921 x -187591-2533 x -142267-16837 x -21403


How do I find the factor combinations of the number 360,362,311?

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 360,362,311, 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.

1 360,362,311
-1 -360,362,311

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 360,362,311.

Example:
1 x 360,362,311 = 360,362,311
and
-1 x -360,362,311 = 360,362,311
Notice both answers equal 360,362,311

With that explanation out of the way, let's continue. Next, we take the number 360,362,311 and divide it by 2:

360,362,311 ÷ 2 = 180,181,155.5

If the quotient is a whole number, then 2 and 180,181,155.5 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:

1 360,362,311
-1 -360,362,311

Now, we try dividing 360,362,311 by 3:

360,362,311 ÷ 3 = 120,120,770.3333

If the quotient is a whole number, then 3 and 120,120,770.3333 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:

1 360,362,311
-1 -360,362,311

Let's try dividing by 4:

360,362,311 ÷ 4 = 90,090,577.75

If the quotient is a whole number, then 4 and 90,090,577.75 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:

1 360,362,311
-1 360,362,311
Keep dividing by the next highest number until you cannot divide anymore.

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

1171131491,2591,9212,53316,83721,403142,267187,591286,2292,418,5393,189,04721,197,783360,362,311
-1-17-113-149-1,259-1,921-2,533-16,837-21,403-142,267-187,591-286,229-2,418,539-3,189,047-21,197,783-360,362,311

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