Q: What are the factor combinations of the number 361,503,121?

 A:
Positive:   1 x 3615031217 x 5164330323 x 1571752731 x 11661391161 x 2245361217 x 1665913713 x 5070174991 x 72431
Negative: -1 x -361503121-7 x -51643303-23 x -15717527-31 x -11661391-161 x -2245361-217 x -1665913-713 x -507017-4991 x -72431


How do I find the factor combinations of the number 361,503,121?

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 361,503,121, 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.

1 361,503,121
-1 -361,503,121

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 361,503,121.

Example:
1 x 361,503,121 = 361,503,121
and
-1 x -361,503,121 = 361,503,121
Notice both answers equal 361,503,121

With that explanation out of the way, let's continue. Next, we take the number 361,503,121 and divide it by 2:

361,503,121 ÷ 2 = 180,751,560.5

If the quotient is a whole number, then 2 and 180,751,560.5 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:

1 361,503,121
-1 -361,503,121

Now, we try dividing 361,503,121 by 3:

361,503,121 ÷ 3 = 120,501,040.3333

If the quotient is a whole number, then 3 and 120,501,040.3333 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:

1 361,503,121
-1 -361,503,121

Let's try dividing by 4:

361,503,121 ÷ 4 = 90,375,780.25

If the quotient is a whole number, then 4 and 90,375,780.25 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:

1 361,503,121
-1 361,503,121
Keep dividing by the next highest number until you cannot divide anymore.

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

1723311612177134,99172,431507,0171,665,9132,245,36111,661,39115,717,52751,643,303361,503,121
-1-7-23-31-161-217-713-4,991-72,431-507,017-1,665,913-2,245,361-11,661,391-15,717,527-51,643,303-361,503,121

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