Q: What are the factor combinations of the number 26,735,009?

 A:
Positive:   1 x 267350097 x 381928773 x 366233113 x 236593463 x 57743511 x 52319791 x 337993241 x 8249
Negative: -1 x -26735009-7 x -3819287-73 x -366233-113 x -236593-463 x -57743-511 x -52319-791 x -33799-3241 x -8249


How do I find the factor combinations of the number 26,735,009?

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 26,735,009, 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 26,735,009
-1 -26,735,009

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 26,735,009.

Example:
1 x 26,735,009 = 26,735,009
and
-1 x -26,735,009 = 26,735,009
Notice both answers equal 26,735,009

With that explanation out of the way, let's continue. Next, we take the number 26,735,009 and divide it by 2:

26,735,009 ÷ 2 = 13,367,504.5

If the quotient is a whole number, then 2 and 13,367,504.5 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 26,735,009
-1 -26,735,009

Now, we try dividing 26,735,009 by 3:

26,735,009 ÷ 3 = 8,911,669.6667

If the quotient is a whole number, then 3 and 8,911,669.6667 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 26,735,009
-1 -26,735,009

Let's try dividing by 4:

26,735,009 ÷ 4 = 6,683,752.25

If the quotient is a whole number, then 4 and 6,683,752.25 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 26,735,009
-1 26,735,009
Keep dividing by the next highest number until you cannot divide anymore.

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

17731134635117913,2418,24933,79952,31957,743236,593366,2333,819,28726,735,009
-1-7-73-113-463-511-791-3,241-8,249-33,799-52,319-57,743-236,593-366,233-3,819,287-26,735,009

More Examples

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