Q: What are the factor combinations of the number 25,623,125?

 A:
Positive:   1 x 256231255 x 512462511 x 232937525 x 102492555 x 465875125 x 204985275 x 93175625 x 409971375 x 186353727 x 6875
Negative: -1 x -25623125-5 x -5124625-11 x -2329375-25 x -1024925-55 x -465875-125 x -204985-275 x -93175-625 x -40997-1375 x -18635-3727 x -6875


How do I find the factor combinations of the number 25,623,125?

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 25,623,125, 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 25,623,125
-1 -25,623,125

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 25,623,125.

Example:
1 x 25,623,125 = 25,623,125
and
-1 x -25,623,125 = 25,623,125
Notice both answers equal 25,623,125

With that explanation out of the way, let's continue. Next, we take the number 25,623,125 and divide it by 2:

25,623,125 ÷ 2 = 12,811,562.5

If the quotient is a whole number, then 2 and 12,811,562.5 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 25,623,125
-1 -25,623,125

Now, we try dividing 25,623,125 by 3:

25,623,125 ÷ 3 = 8,541,041.6667

If the quotient is a whole number, then 3 and 8,541,041.6667 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 25,623,125
-1 -25,623,125

Let's try dividing by 4:

25,623,125 ÷ 4 = 6,405,781.25

If the quotient is a whole number, then 4 and 6,405,781.25 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 25,623,125
-1 25,623,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252756251,3753,7276,87518,63540,99793,175204,985465,8751,024,9252,329,3755,124,62525,623,125
-1-5-11-25-55-125-275-625-1,375-3,727-6,875-18,635-40,997-93,175-204,985-465,875-1,024,925-2,329,375-5,124,625-25,623,125

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