Q: What are the factor combinations of the number 27,009,275?

 A:
Positive:   1 x 270092755 x 540185525 x 108037161 x 44277589 x 303475199 x 135725305 x 88555445 x 60695995 x 271451525 x 177112225 x 121394975 x 5429
Negative: -1 x -27009275-5 x -5401855-25 x -1080371-61 x -442775-89 x -303475-199 x -135725-305 x -88555-445 x -60695-995 x -27145-1525 x -17711-2225 x -12139-4975 x -5429


How do I find the factor combinations of the number 27,009,275?

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 27,009,275, 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 27,009,275
-1 -27,009,275

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 27,009,275.

Example:
1 x 27,009,275 = 27,009,275
and
-1 x -27,009,275 = 27,009,275
Notice both answers equal 27,009,275

With that explanation out of the way, let's continue. Next, we take the number 27,009,275 and divide it by 2:

27,009,275 ÷ 2 = 13,504,637.5

If the quotient is a whole number, then 2 and 13,504,637.5 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 27,009,275
-1 -27,009,275

Now, we try dividing 27,009,275 by 3:

27,009,275 ÷ 3 = 9,003,091.6667

If the quotient is a whole number, then 3 and 9,003,091.6667 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 27,009,275
-1 -27,009,275

Let's try dividing by 4:

27,009,275 ÷ 4 = 6,752,318.75

If the quotient is a whole number, then 4 and 6,752,318.75 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 27,009,275
-1 27,009,275
Keep dividing by the next highest number until you cannot divide anymore.

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

152561891993054459951,5252,2254,9755,42912,13917,71127,14560,69588,555135,725303,475442,7751,080,3715,401,85527,009,275
-1-5-25-61-89-199-305-445-995-1,525-2,225-4,975-5,429-12,139-17,711-27,145-60,695-88,555-135,725-303,475-442,775-1,080,371-5,401,855-27,009,275

More Examples

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