Q: What are the factor combinations of the number 36,315,517?

 A:
Positive:   1 x 363155177 x 518793119 x 191134349 x 741133133 x 273049361 x 100597931 x 390072053 x 176892527 x 14371
Negative: -1 x -36315517-7 x -5187931-19 x -1911343-49 x -741133-133 x -273049-361 x -100597-931 x -39007-2053 x -17689-2527 x -14371


How do I find the factor combinations of the number 36,315,517?

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 36,315,517, 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 36,315,517
-1 -36,315,517

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 36,315,517.

Example:
1 x 36,315,517 = 36,315,517
and
-1 x -36,315,517 = 36,315,517
Notice both answers equal 36,315,517

With that explanation out of the way, let's continue. Next, we take the number 36,315,517 and divide it by 2:

36,315,517 ÷ 2 = 18,157,758.5

If the quotient is a whole number, then 2 and 18,157,758.5 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 36,315,517
-1 -36,315,517

Now, we try dividing 36,315,517 by 3:

36,315,517 ÷ 3 = 12,105,172.3333

If the quotient is a whole number, then 3 and 12,105,172.3333 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 36,315,517
-1 -36,315,517

Let's try dividing by 4:

36,315,517 ÷ 4 = 9,078,879.25

If the quotient is a whole number, then 4 and 9,078,879.25 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 36,315,517
-1 36,315,517
Keep dividing by the next highest number until you cannot divide anymore.

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

1719491333619312,0532,52714,37117,68939,007100,597273,049741,1331,911,3435,187,93136,315,517
-1-7-19-49-133-361-931-2,053-2,527-14,371-17,689-39,007-100,597-273,049-741,133-1,911,343-5,187,931-36,315,517

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