Q: What are the factor combinations of the number 32,684,659?

 A:
Positive:   1 x 326846597 x 466923717 x 1922627119 x 274661
Negative: -1 x -32684659-7 x -4669237-17 x -1922627-119 x -274661


How do I find the factor combinations of the number 32,684,659?

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 32,684,659, 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 32,684,659
-1 -32,684,659

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 32,684,659.

Example:
1 x 32,684,659 = 32,684,659
and
-1 x -32,684,659 = 32,684,659
Notice both answers equal 32,684,659

With that explanation out of the way, let's continue. Next, we take the number 32,684,659 and divide it by 2:

32,684,659 ÷ 2 = 16,342,329.5

If the quotient is a whole number, then 2 and 16,342,329.5 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 32,684,659
-1 -32,684,659

Now, we try dividing 32,684,659 by 3:

32,684,659 ÷ 3 = 10,894,886.3333

If the quotient is a whole number, then 3 and 10,894,886.3333 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 32,684,659
-1 -32,684,659

Let's try dividing by 4:

32,684,659 ÷ 4 = 8,171,164.75

If the quotient is a whole number, then 4 and 8,171,164.75 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 32,684,659
-1 32,684,659
Keep dividing by the next highest number until you cannot divide anymore.

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

1717119274,6611,922,6274,669,23732,684,659
-1-7-17-119-274,661-1,922,627-4,669,237-32,684,659

More Examples

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