Q: What are the factor combinations of the number 105,152,327?

 A:
Positive:   1 x 1051523277 x 1502176117 x 618543119 x 5534333119 x 883633133 x 790619323 x 3255492261 x 46507
Negative: -1 x -105152327-7 x -15021761-17 x -6185431-19 x -5534333-119 x -883633-133 x -790619-323 x -325549-2261 x -46507


How do I find the factor combinations of the number 105,152,327?

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 105,152,327, 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.

1 105,152,327
-1 -105,152,327

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 105,152,327.

Example:
1 x 105,152,327 = 105,152,327
and
-1 x -105,152,327 = 105,152,327
Notice both answers equal 105,152,327

With that explanation out of the way, let's continue. Next, we take the number 105,152,327 and divide it by 2:

105,152,327 ÷ 2 = 52,576,163.5

If the quotient is a whole number, then 2 and 52,576,163.5 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:

1 105,152,327
-1 -105,152,327

Now, we try dividing 105,152,327 by 3:

105,152,327 ÷ 3 = 35,050,775.6667

If the quotient is a whole number, then 3 and 35,050,775.6667 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:

1 105,152,327
-1 -105,152,327

Let's try dividing by 4:

105,152,327 ÷ 4 = 26,288,081.75

If the quotient is a whole number, then 4 and 26,288,081.75 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:

1 105,152,327
-1 105,152,327
Keep dividing by the next highest number until you cannot divide anymore.

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

1717191191333232,26146,507325,549790,619883,6335,534,3336,185,43115,021,761105,152,327
-1-7-17-19-119-133-323-2,261-46,507-325,549-790,619-883,633-5,534,333-6,185,431-15,021,761-105,152,327

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