Q: What are the factor combinations of the number 36,315,229?

 A:
Positive:   1 x 3631522923 x 157892331 x 117145953 x 685193713 x 50933961 x 377891219 x 297911643 x 22103
Negative: -1 x -36315229-23 x -1578923-31 x -1171459-53 x -685193-713 x -50933-961 x -37789-1219 x -29791-1643 x -22103


How do I find the factor combinations of the number 36,315,229?

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 36,315,229, 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 36,315,229
-1 -36,315,229

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 36,315,229.

Example:
1 x 36,315,229 = 36,315,229
and
-1 x -36,315,229 = 36,315,229
Notice both answers equal 36,315,229

With that explanation out of the way, let's continue. Next, we take the number 36,315,229 and divide it by 2:

36,315,229 ÷ 2 = 18,157,614.5

If the quotient is a whole number, then 2 and 18,157,614.5 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 36,315,229
-1 -36,315,229

Now, we try dividing 36,315,229 by 3:

36,315,229 ÷ 3 = 12,105,076.3333

If the quotient is a whole number, then 3 and 12,105,076.3333 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 36,315,229
-1 -36,315,229

Let's try dividing by 4:

36,315,229 ÷ 4 = 9,078,807.25

If the quotient is a whole number, then 4 and 9,078,807.25 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 36,315,229
-1 36,315,229
Keep dividing by the next highest number until you cannot divide anymore.

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

12331537139611,2191,64322,10329,79137,78950,933685,1931,171,4591,578,92336,315,229
-1-23-31-53-713-961-1,219-1,643-22,103-29,791-37,789-50,933-685,193-1,171,459-1,578,923-36,315,229

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