Q: What are the factor combinations of the number 25,500,145?

 A:
Positive:   1 x 255001455 x 510002911 x 231819555 x 463639113 x 225665121 x 210745373 x 68365565 x 45133605 x 421491243 x 205151865 x 136734103 x 6215
Negative: -1 x -25500145-5 x -5100029-11 x -2318195-55 x -463639-113 x -225665-121 x -210745-373 x -68365-565 x -45133-605 x -42149-1243 x -20515-1865 x -13673-4103 x -6215


How do I find the factor combinations of the number 25,500,145?

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 25,500,145, 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 25,500,145
-1 -25,500,145

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 25,500,145.

Example:
1 x 25,500,145 = 25,500,145
and
-1 x -25,500,145 = 25,500,145
Notice both answers equal 25,500,145

With that explanation out of the way, let's continue. Next, we take the number 25,500,145 and divide it by 2:

25,500,145 ÷ 2 = 12,750,072.5

If the quotient is a whole number, then 2 and 12,750,072.5 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 25,500,145
-1 -25,500,145

Now, we try dividing 25,500,145 by 3:

25,500,145 ÷ 3 = 8,500,048.3333

If the quotient is a whole number, then 3 and 8,500,048.3333 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 25,500,145
-1 -25,500,145

Let's try dividing by 4:

25,500,145 ÷ 4 = 6,375,036.25

If the quotient is a whole number, then 4 and 6,375,036.25 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 25,500,145
-1 25,500,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551131213735656051,2431,8654,1036,21513,67320,51542,14945,13368,365210,745225,665463,6392,318,1955,100,02925,500,145
-1-5-11-55-113-121-373-565-605-1,243-1,865-4,103-6,215-13,673-20,515-42,149-45,133-68,365-210,745-225,665-463,639-2,318,195-5,100,029-25,500,145

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