Q: What are the factor combinations of the number 412,156,325?

 A:
Positive:   1 x 4121563255 x 824312657 x 5887947525 x 1648625335 x 11775895175 x 2355179193 x 2135525965 x 4271051351 x 3050754825 x 854216755 x 6101512203 x 33775
Negative: -1 x -412156325-5 x -82431265-7 x -58879475-25 x -16486253-35 x -11775895-175 x -2355179-193 x -2135525-965 x -427105-1351 x -305075-4825 x -85421-6755 x -61015-12203 x -33775


How do I find the factor combinations of the number 412,156,325?

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 412,156,325, 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.

1 412,156,325
-1 -412,156,325

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 412,156,325.

Example:
1 x 412,156,325 = 412,156,325
and
-1 x -412,156,325 = 412,156,325
Notice both answers equal 412,156,325

With that explanation out of the way, let's continue. Next, we take the number 412,156,325 and divide it by 2:

412,156,325 ÷ 2 = 206,078,162.5

If the quotient is a whole number, then 2 and 206,078,162.5 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:

1 412,156,325
-1 -412,156,325

Now, we try dividing 412,156,325 by 3:

412,156,325 ÷ 3 = 137,385,441.6667

If the quotient is a whole number, then 3 and 137,385,441.6667 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:

1 412,156,325
-1 -412,156,325

Let's try dividing by 4:

412,156,325 ÷ 4 = 103,039,081.25

If the quotient is a whole number, then 4 and 103,039,081.25 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:

1 412,156,325
-1 412,156,325
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351751939651,3514,8256,75512,20333,77561,01585,421305,075427,1052,135,5252,355,17911,775,89516,486,25358,879,47582,431,265412,156,325
-1-5-7-25-35-175-193-965-1,351-4,825-6,755-12,203-33,775-61,015-85,421-305,075-427,105-2,135,525-2,355,179-11,775,895-16,486,253-58,879,475-82,431,265-412,156,325

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