Q: What are the factor combinations of the number 165,266,525?

 A:
Positive:   1 x 1652665255 x 3305330525 x 661066173 x 2263925137 x 1206325365 x 452785661 x 250025685 x 2412651825 x 905573305 x 500053425 x 4825310001 x 16525
Negative: -1 x -165266525-5 x -33053305-25 x -6610661-73 x -2263925-137 x -1206325-365 x -452785-661 x -250025-685 x -241265-1825 x -90557-3305 x -50005-3425 x -48253-10001 x -16525


How do I find the factor combinations of the number 165,266,525?

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 165,266,525, 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.

1 165,266,525
-1 -165,266,525

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 165,266,525.

Example:
1 x 165,266,525 = 165,266,525
and
-1 x -165,266,525 = 165,266,525
Notice both answers equal 165,266,525

With that explanation out of the way, let's continue. Next, we take the number 165,266,525 and divide it by 2:

165,266,525 ÷ 2 = 82,633,262.5

If the quotient is a whole number, then 2 and 82,633,262.5 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:

1 165,266,525
-1 -165,266,525

Now, we try dividing 165,266,525 by 3:

165,266,525 ÷ 3 = 55,088,841.6667

If the quotient is a whole number, then 3 and 55,088,841.6667 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:

1 165,266,525
-1 -165,266,525

Let's try dividing by 4:

165,266,525 ÷ 4 = 41,316,631.25

If the quotient is a whole number, then 4 and 41,316,631.25 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:

1 165,266,525
-1 165,266,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1525731373656616851,8253,3053,42510,00116,52548,25350,00590,557241,265250,025452,7851,206,3252,263,9256,610,66133,053,305165,266,525
-1-5-25-73-137-365-661-685-1,825-3,305-3,425-10,001-16,525-48,253-50,005-90,557-241,265-250,025-452,785-1,206,325-2,263,925-6,610,661-33,053,305-165,266,525

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