Q: What are the factor combinations of the number 205,016,225?

 A:
Positive:   1 x 2050162255 x 4100324525 x 820064929 x 706952583 x 2470075145 x 1413905415 x 494015725 x 2827812075 x 988032407 x 851753407 x 6017512035 x 17035
Negative: -1 x -205016225-5 x -41003245-25 x -8200649-29 x -7069525-83 x -2470075-145 x -1413905-415 x -494015-725 x -282781-2075 x -98803-2407 x -85175-3407 x -60175-12035 x -17035


How do I find the factor combinations of the number 205,016,225?

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 205,016,225, 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.

1 205,016,225
-1 -205,016,225

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 205,016,225.

Example:
1 x 205,016,225 = 205,016,225
and
-1 x -205,016,225 = 205,016,225
Notice both answers equal 205,016,225

With that explanation out of the way, let's continue. Next, we take the number 205,016,225 and divide it by 2:

205,016,225 ÷ 2 = 102,508,112.5

If the quotient is a whole number, then 2 and 102,508,112.5 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:

1 205,016,225
-1 -205,016,225

Now, we try dividing 205,016,225 by 3:

205,016,225 ÷ 3 = 68,338,741.6667

If the quotient is a whole number, then 3 and 68,338,741.6667 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:

1 205,016,225
-1 -205,016,225

Let's try dividing by 4:

205,016,225 ÷ 4 = 51,254,056.25

If the quotient is a whole number, then 4 and 51,254,056.25 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:

1 205,016,225
-1 205,016,225
Keep dividing by the next highest number until you cannot divide anymore.

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

152529831454157252,0752,4073,40712,03517,03560,17585,17598,803282,781494,0151,413,9052,470,0757,069,5258,200,64941,003,245205,016,225
-1-5-25-29-83-145-415-725-2,075-2,407-3,407-12,035-17,035-60,175-85,175-98,803-282,781-494,015-1,413,905-2,470,075-7,069,525-8,200,649-41,003,245-205,016,225

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