Q: What are the factor combinations of the number 744,107?

 A:
Positive:   1 x 7441077 x 10630113 x 5723917 x 4377137 x 2011191 x 8177119 x 6253169 x 4403221 x 3367259 x 2873481 x 1547629 x 1183
Negative: -1 x -744107-7 x -106301-13 x -57239-17 x -43771-37 x -20111-91 x -8177-119 x -6253-169 x -4403-221 x -3367-259 x -2873-481 x -1547-629 x -1183


How do I find the factor combinations of the number 744,107?

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 744,107, 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.

1 744,107
-1 -744,107

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 744,107.

Example:
1 x 744,107 = 744,107
and
-1 x -744,107 = 744,107
Notice both answers equal 744,107

With that explanation out of the way, let's continue. Next, we take the number 744,107 and divide it by 2:

744,107 ÷ 2 = 372,053.5

If the quotient is a whole number, then 2 and 372,053.5 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:

1 744,107
-1 -744,107

Now, we try dividing 744,107 by 3:

744,107 ÷ 3 = 248,035.6667

If the quotient is a whole number, then 3 and 248,035.6667 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:

1 744,107
-1 -744,107

Let's try dividing by 4:

744,107 ÷ 4 = 186,026.75

If the quotient is a whole number, then 4 and 186,026.75 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:

1 744,107
-1 744,107
Keep dividing by the next highest number until you cannot divide anymore.

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

17131737911191692212594816291,1831,5472,8733,3674,4036,2538,17720,11143,77157,239106,301744,107
-1-7-13-17-37-91-119-169-221-259-481-629-1,183-1,547-2,873-3,367-4,403-6,253-8,177-20,111-43,771-57,239-106,301-744,107

More Examples

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