Q: What are the factor combinations of the number 643,736?

 A:
Positive:   1 x 6437362 x 3218684 x 1609348 x 8046767 x 9608134 x 4804268 x 2402536 x 1201
Negative: -1 x -643736-2 x -321868-4 x -160934-8 x -80467-67 x -9608-134 x -4804-268 x -2402-536 x -1201


How do I find the factor combinations of the number 643,736?

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 643,736, 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.

1 643,736
-1 -643,736

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 643,736.

Example:
1 x 643,736 = 643,736
and
-1 x -643,736 = 643,736
Notice both answers equal 643,736

With that explanation out of the way, let's continue. Next, we take the number 643,736 and divide it by 2:

643,736 ÷ 2 = 321,868

If the quotient is a whole number, then 2 and 321,868 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 2 321,868 643,736
-1 -2 -321,868 -643,736

Now, we try dividing 643,736 by 3:

643,736 ÷ 3 = 214,578.6667

If the quotient is a whole number, then 3 and 214,578.6667 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 2 321,868 643,736
-1 -2 -321,868 -643,736

Let's try dividing by 4:

643,736 ÷ 4 = 160,934

If the quotient is a whole number, then 4 and 160,934 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 4 160,934 321,868 643,736
-1 -2 -4 -160,934 -321,868 643,736
Keep dividing by the next highest number until you cannot divide anymore.

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

1248671342685361,2012,4024,8049,60880,467160,934321,868643,736
-1-2-4-8-67-134-268-536-1,201-2,402-4,804-9,608-80,467-160,934-321,868-643,736

More Examples

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