Q: What are the factor combinations of the number 27,122,735?

 A:
Positive:   1 x 271227355 x 542454717 x 159545561 x 44463585 x 319091305 x 889271037 x 261555185 x 5231
Negative: -1 x -27122735-5 x -5424547-17 x -1595455-61 x -444635-85 x -319091-305 x -88927-1037 x -26155-5185 x -5231


How do I find the factor combinations of the number 27,122,735?

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 27,122,735, 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 27,122,735
-1 -27,122,735

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 27,122,735.

Example:
1 x 27,122,735 = 27,122,735
and
-1 x -27,122,735 = 27,122,735
Notice both answers equal 27,122,735

With that explanation out of the way, let's continue. Next, we take the number 27,122,735 and divide it by 2:

27,122,735 ÷ 2 = 13,561,367.5

If the quotient is a whole number, then 2 and 13,561,367.5 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 27,122,735
-1 -27,122,735

Now, we try dividing 27,122,735 by 3:

27,122,735 ÷ 3 = 9,040,911.6667

If the quotient is a whole number, then 3 and 9,040,911.6667 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 27,122,735
-1 -27,122,735

Let's try dividing by 4:

27,122,735 ÷ 4 = 6,780,683.75

If the quotient is a whole number, then 4 and 6,780,683.75 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 27,122,735
-1 27,122,735
Keep dividing by the next highest number until you cannot divide anymore.

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

151761853051,0375,1855,23126,15588,927319,091444,6351,595,4555,424,54727,122,735
-1-5-17-61-85-305-1,037-5,185-5,231-26,155-88,927-319,091-444,635-1,595,455-5,424,547-27,122,735

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