Q: What are the factor combinations of the number 25,361,165?

 A:
Positive:   1 x 253611655 x 507223341 x 618565193 x 131405205 x 123713641 x 39565965 x 262813205 x 7913
Negative: -1 x -25361165-5 x -5072233-41 x -618565-193 x -131405-205 x -123713-641 x -39565-965 x -26281-3205 x -7913


How do I find the factor combinations of the number 25,361,165?

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 25,361,165, 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 25,361,165
-1 -25,361,165

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 25,361,165.

Example:
1 x 25,361,165 = 25,361,165
and
-1 x -25,361,165 = 25,361,165
Notice both answers equal 25,361,165

With that explanation out of the way, let's continue. Next, we take the number 25,361,165 and divide it by 2:

25,361,165 ÷ 2 = 12,680,582.5

If the quotient is a whole number, then 2 and 12,680,582.5 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 25,361,165
-1 -25,361,165

Now, we try dividing 25,361,165 by 3:

25,361,165 ÷ 3 = 8,453,721.6667

If the quotient is a whole number, then 3 and 8,453,721.6667 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 25,361,165
-1 -25,361,165

Let's try dividing by 4:

25,361,165 ÷ 4 = 6,340,291.25

If the quotient is a whole number, then 4 and 6,340,291.25 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 25,361,165
-1 25,361,165
Keep dividing by the next highest number until you cannot divide anymore.

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

15411932056419653,2057,91326,28139,565123,713131,405618,5655,072,23325,361,165
-1-5-41-193-205-641-965-3,205-7,913-26,281-39,565-123,713-131,405-618,565-5,072,233-25,361,165

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