Q: What are the factor combinations of the number 150,106,177?

 A:
Positive:   1 x 15010617713 x 1154662961 x 246075773 x 2056249793 x 189289949 x 1581732593 x 578894453 x 33709
Negative: -1 x -150106177-13 x -11546629-61 x -2460757-73 x -2056249-793 x -189289-949 x -158173-2593 x -57889-4453 x -33709


How do I find the factor combinations of the number 150,106,177?

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 150,106,177, 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.

1 150,106,177
-1 -150,106,177

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 150,106,177.

Example:
1 x 150,106,177 = 150,106,177
and
-1 x -150,106,177 = 150,106,177
Notice both answers equal 150,106,177

With that explanation out of the way, let's continue. Next, we take the number 150,106,177 and divide it by 2:

150,106,177 ÷ 2 = 75,053,088.5

If the quotient is a whole number, then 2 and 75,053,088.5 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:

1 150,106,177
-1 -150,106,177

Now, we try dividing 150,106,177 by 3:

150,106,177 ÷ 3 = 50,035,392.3333

If the quotient is a whole number, then 3 and 50,035,392.3333 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:

1 150,106,177
-1 -150,106,177

Let's try dividing by 4:

150,106,177 ÷ 4 = 37,526,544.25

If the quotient is a whole number, then 4 and 37,526,544.25 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:

1 150,106,177
-1 150,106,177
Keep dividing by the next highest number until you cannot divide anymore.

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

11361737939492,5934,45333,70957,889158,173189,2892,056,2492,460,75711,546,629150,106,177
-1-13-61-73-793-949-2,593-4,453-33,709-57,889-158,173-189,289-2,056,249-2,460,757-11,546,629-150,106,177

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