Q: What are the factor combinations of the number 27,909,739?

 A:
Positive:   1 x 2790973911 x 253724913 x 2146903121 x 230659143 x 1951731331 x 209691573 x 177431613 x 17303
Negative: -1 x -27909739-11 x -2537249-13 x -2146903-121 x -230659-143 x -195173-1331 x -20969-1573 x -17743-1613 x -17303


How do I find the factor combinations of the number 27,909,739?

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 27,909,739, 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 27,909,739
-1 -27,909,739

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 27,909,739.

Example:
1 x 27,909,739 = 27,909,739
and
-1 x -27,909,739 = 27,909,739
Notice both answers equal 27,909,739

With that explanation out of the way, let's continue. Next, we take the number 27,909,739 and divide it by 2:

27,909,739 ÷ 2 = 13,954,869.5

If the quotient is a whole number, then 2 and 13,954,869.5 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 27,909,739
-1 -27,909,739

Now, we try dividing 27,909,739 by 3:

27,909,739 ÷ 3 = 9,303,246.3333

If the quotient is a whole number, then 3 and 9,303,246.3333 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 27,909,739
-1 -27,909,739

Let's try dividing by 4:

27,909,739 ÷ 4 = 6,977,434.75

If the quotient is a whole number, then 4 and 6,977,434.75 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 27,909,739
-1 27,909,739
Keep dividing by the next highest number until you cannot divide anymore.

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

111131211431,3311,5731,61317,30317,74320,969195,173230,6592,146,9032,537,24927,909,739
-1-11-13-121-143-1,331-1,573-1,613-17,303-17,743-20,969-195,173-230,659-2,146,903-2,537,249-27,909,739

More Examples

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