Q: What are the factor combinations of the number 738,395?

 A:
Positive:   1 x 7383955 x 1476797 x 10548517 x 4343535 x 2109773 x 1011585 x 8687119 x 6205289 x 2555365 x 2023511 x 1445595 x 1241
Negative: -1 x -738395-5 x -147679-7 x -105485-17 x -43435-35 x -21097-73 x -10115-85 x -8687-119 x -6205-289 x -2555-365 x -2023-511 x -1445-595 x -1241


How do I find the factor combinations of the number 738,395?

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 738,395, 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.

1 738,395
-1 -738,395

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 738,395.

Example:
1 x 738,395 = 738,395
and
-1 x -738,395 = 738,395
Notice both answers equal 738,395

With that explanation out of the way, let's continue. Next, we take the number 738,395 and divide it by 2:

738,395 ÷ 2 = 369,197.5

If the quotient is a whole number, then 2 and 369,197.5 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:

1 738,395
-1 -738,395

Now, we try dividing 738,395 by 3:

738,395 ÷ 3 = 246,131.6667

If the quotient is a whole number, then 3 and 246,131.6667 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:

1 738,395
-1 -738,395

Let's try dividing by 4:

738,395 ÷ 4 = 184,598.75

If the quotient is a whole number, then 4 and 184,598.75 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:

1 738,395
-1 738,395
Keep dividing by the next highest number until you cannot divide anymore.

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

157173573851192893655115951,2411,4452,0232,5556,2058,68710,11521,09743,435105,485147,679738,395
-1-5-7-17-35-73-85-119-289-365-511-595-1,241-1,445-2,023-2,555-6,205-8,687-10,115-21,097-43,435-105,485-147,679-738,395

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