Q: What are the factor combinations of the number 733,617,642?

 A:
Positive:   1 x 7336176422 x 3668088213 x 2445392146 x 12226960747 x 1560888694 x 7804443141 x 5202962282 x 2601481
Negative: -1 x -733617642-2 x -366808821-3 x -244539214-6 x -122269607-47 x -15608886-94 x -7804443-141 x -5202962-282 x -2601481


How do I find the factor combinations of the number 733,617,642?

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 733,617,642, 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.

1 733,617,642
-1 -733,617,642

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 733,617,642.

Example:
1 x 733,617,642 = 733,617,642
and
-1 x -733,617,642 = 733,617,642
Notice both answers equal 733,617,642

With that explanation out of the way, let's continue. Next, we take the number 733,617,642 and divide it by 2:

733,617,642 ÷ 2 = 366,808,821

If the quotient is a whole number, then 2 and 366,808,821 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 366,808,821 733,617,642
-1 -2 -366,808,821 -733,617,642

Now, we try dividing 733,617,642 by 3:

733,617,642 ÷ 3 = 244,539,214

If the quotient is a whole number, then 3 and 244,539,214 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 244,539,214 366,808,821 733,617,642
-1 -2 -3 -244,539,214 -366,808,821 -733,617,642

Let's try dividing by 4:

733,617,642 ÷ 4 = 183,404,410.5

If the quotient is a whole number, then 4 and 183,404,410.5 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 2 3 244,539,214 366,808,821 733,617,642
-1 -2 -3 -244,539,214 -366,808,821 733,617,642
Keep dividing by the next highest number until you cannot divide anymore.

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

123647941412822,601,4815,202,9627,804,44315,608,886122,269,607244,539,214366,808,821733,617,642
-1-2-3-6-47-94-141-282-2,601,481-5,202,962-7,804,443-15,608,886-122,269,607-244,539,214-366,808,821-733,617,642

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