Q: What are the factor combinations of the number 150,513,025?

 A:
Positive:   1 x 1505130255 x 3010260513 x 1157792525 x 602052165 x 2315585151 x 996775325 x 463117755 x 1993551963 x 766753067 x 490753775 x 398719815 x 15335
Negative: -1 x -150513025-5 x -30102605-13 x -11577925-25 x -6020521-65 x -2315585-151 x -996775-325 x -463117-755 x -199355-1963 x -76675-3067 x -49075-3775 x -39871-9815 x -15335


How do I find the factor combinations of the number 150,513,025?

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 150,513,025, 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.

1 150,513,025
-1 -150,513,025

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 150,513,025.

Example:
1 x 150,513,025 = 150,513,025
and
-1 x -150,513,025 = 150,513,025
Notice both answers equal 150,513,025

With that explanation out of the way, let's continue. Next, we take the number 150,513,025 and divide it by 2:

150,513,025 ÷ 2 = 75,256,512.5

If the quotient is a whole number, then 2 and 75,256,512.5 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:

1 150,513,025
-1 -150,513,025

Now, we try dividing 150,513,025 by 3:

150,513,025 ÷ 3 = 50,171,008.3333

If the quotient is a whole number, then 3 and 50,171,008.3333 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:

1 150,513,025
-1 -150,513,025

Let's try dividing by 4:

150,513,025 ÷ 4 = 37,628,256.25

If the quotient is a whole number, then 4 and 37,628,256.25 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:

1 150,513,025
-1 150,513,025
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651513257551,9633,0673,7759,81515,33539,87149,07576,675199,355463,117996,7752,315,5856,020,52111,577,92530,102,605150,513,025
-1-5-13-25-65-151-325-755-1,963-3,067-3,775-9,815-15,335-39,871-49,075-76,675-199,355-463,117-996,775-2,315,585-6,020,521-11,577,925-30,102,605-150,513,025

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