Q: What are the factor combinations of the number 135,216,503?

 A:
Positive:   1 x 135216503
Negative: -1 x -135216503


How do I find the factor combinations of the number 135,216,503?

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 135,216,503, 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.

1 135,216,503
-1 -135,216,503

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 135,216,503.

Example:
1 x 135,216,503 = 135,216,503
and
-1 x -135,216,503 = 135,216,503
Notice both answers equal 135,216,503

With that explanation out of the way, let's continue. Next, we take the number 135,216,503 and divide it by 2:

135,216,503 ÷ 2 = 67,608,251.5

If the quotient is a whole number, then 2 and 67,608,251.5 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:

1 135,216,503
-1 -135,216,503

Now, we try dividing 135,216,503 by 3:

135,216,503 ÷ 3 = 45,072,167.6667

If the quotient is a whole number, then 3 and 45,072,167.6667 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:

1 135,216,503
-1 -135,216,503

Let's try dividing by 4:

135,216,503 ÷ 4 = 33,804,125.75

If the quotient is a whole number, then 4 and 33,804,125.75 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:

1 135,216,503
-1 135,216,503
Keep dividing by the next highest number until you cannot divide anymore.

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

1135,216,503
-1-135,216,503

More Examples

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