Q: What are the factor combinations of the number 25,542,125?

 A:
Positive:   1 x 255421255 x 51084257 x 364887525 x 102168535 x 729775125 x 204337175 x 145955875 x 29191
Negative: -1 x -25542125-5 x -5108425-7 x -3648875-25 x -1021685-35 x -729775-125 x -204337-175 x -145955-875 x -29191


How do I find the factor combinations of the number 25,542,125?

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 25,542,125, 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 25,542,125
-1 -25,542,125

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 25,542,125.

Example:
1 x 25,542,125 = 25,542,125
and
-1 x -25,542,125 = 25,542,125
Notice both answers equal 25,542,125

With that explanation out of the way, let's continue. Next, we take the number 25,542,125 and divide it by 2:

25,542,125 ÷ 2 = 12,771,062.5

If the quotient is a whole number, then 2 and 12,771,062.5 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 25,542,125
-1 -25,542,125

Now, we try dividing 25,542,125 by 3:

25,542,125 ÷ 3 = 8,514,041.6667

If the quotient is a whole number, then 3 and 8,514,041.6667 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 25,542,125
-1 -25,542,125

Let's try dividing by 4:

25,542,125 ÷ 4 = 6,385,531.25

If the quotient is a whole number, then 4 and 6,385,531.25 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 25,542,125
-1 25,542,125
Keep dividing by the next highest number until you cannot divide anymore.

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

157253512517587529,191145,955204,337729,7751,021,6853,648,8755,108,42525,542,125
-1-5-7-25-35-125-175-875-29,191-145,955-204,337-729,775-1,021,685-3,648,875-5,108,425-25,542,125

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