Q: What are the factor combinations of the number 25,023,625?

 A:
Positive:   1 x 250236255 x 500472511 x 227487525 x 100094555 x 454975125 x 200189275 x 909951375 x 18199
Negative: -1 x -25023625-5 x -5004725-11 x -2274875-25 x -1000945-55 x -454975-125 x -200189-275 x -90995-1375 x -18199


How do I find the factor combinations of the number 25,023,625?

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 25,023,625, 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 25,023,625
-1 -25,023,625

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 25,023,625.

Example:
1 x 25,023,625 = 25,023,625
and
-1 x -25,023,625 = 25,023,625
Notice both answers equal 25,023,625

With that explanation out of the way, let's continue. Next, we take the number 25,023,625 and divide it by 2:

25,023,625 ÷ 2 = 12,511,812.5

If the quotient is a whole number, then 2 and 12,511,812.5 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 25,023,625
-1 -25,023,625

Now, we try dividing 25,023,625 by 3:

25,023,625 ÷ 3 = 8,341,208.3333

If the quotient is a whole number, then 3 and 8,341,208.3333 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 25,023,625
-1 -25,023,625

Let's try dividing by 4:

25,023,625 ÷ 4 = 6,255,906.25

If the quotient is a whole number, then 4 and 6,255,906.25 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 25,023,625
-1 25,023,625
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252751,37518,19990,995200,189454,9751,000,9452,274,8755,004,72525,023,625
-1-5-11-25-55-125-275-1,375-18,199-90,995-200,189-454,975-1,000,945-2,274,875-5,004,725-25,023,625

More Examples

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