Q: What are the factor combinations of the number 150,112,025?

 A:
Positive:   1 x 1501120255 x 300224057 x 2144457525 x 600448135 x 4288915113 x 1328425175 x 857783565 x 265685791 x 1897752825 x 531373955 x 379557591 x 19775
Negative: -1 x -150112025-5 x -30022405-7 x -21444575-25 x -6004481-35 x -4288915-113 x -1328425-175 x -857783-565 x -265685-791 x -189775-2825 x -53137-3955 x -37955-7591 x -19775


How do I find the factor combinations of the number 150,112,025?

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 150,112,025, 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.

1 150,112,025
-1 -150,112,025

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 150,112,025.

Example:
1 x 150,112,025 = 150,112,025
and
-1 x -150,112,025 = 150,112,025
Notice both answers equal 150,112,025

With that explanation out of the way, let's continue. Next, we take the number 150,112,025 and divide it by 2:

150,112,025 ÷ 2 = 75,056,012.5

If the quotient is a whole number, then 2 and 75,056,012.5 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:

1 150,112,025
-1 -150,112,025

Now, we try dividing 150,112,025 by 3:

150,112,025 ÷ 3 = 50,037,341.6667

If the quotient is a whole number, then 3 and 50,037,341.6667 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:

1 150,112,025
-1 -150,112,025

Let's try dividing by 4:

150,112,025 ÷ 4 = 37,528,006.25

If the quotient is a whole number, then 4 and 37,528,006.25 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:

1 150,112,025
-1 150,112,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351131755657912,8253,9557,59119,77537,95553,137189,775265,685857,7831,328,4254,288,9156,004,48121,444,57530,022,405150,112,025
-1-5-7-25-35-113-175-565-791-2,825-3,955-7,591-19,775-37,955-53,137-189,775-265,685-857,783-1,328,425-4,288,915-6,004,481-21,444,575-30,022,405-150,112,025

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