Q: What are the factor combinations of the number 46,523,659?

 A:
Positive:   1 x 465236597 x 664623713 x 357874391 x 511249461 x 1009191109 x 419513227 x 144175993 x 7763
Negative: -1 x -46523659-7 x -6646237-13 x -3578743-91 x -511249-461 x -100919-1109 x -41951-3227 x -14417-5993 x -7763


How do I find the factor combinations of the number 46,523,659?

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 46,523,659, 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 46,523,659
-1 -46,523,659

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 46,523,659.

Example:
1 x 46,523,659 = 46,523,659
and
-1 x -46,523,659 = 46,523,659
Notice both answers equal 46,523,659

With that explanation out of the way, let's continue. Next, we take the number 46,523,659 and divide it by 2:

46,523,659 ÷ 2 = 23,261,829.5

If the quotient is a whole number, then 2 and 23,261,829.5 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 46,523,659
-1 -46,523,659

Now, we try dividing 46,523,659 by 3:

46,523,659 ÷ 3 = 15,507,886.3333

If the quotient is a whole number, then 3 and 15,507,886.3333 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 46,523,659
-1 -46,523,659

Let's try dividing by 4:

46,523,659 ÷ 4 = 11,630,914.75

If the quotient is a whole number, then 4 and 11,630,914.75 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 46,523,659
-1 46,523,659
Keep dividing by the next highest number until you cannot divide anymore.

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

1713914611,1093,2275,9937,76314,41741,951100,919511,2493,578,7436,646,23746,523,659
-1-7-13-91-461-1,109-3,227-5,993-7,763-14,417-41,951-100,919-511,249-3,578,743-6,646,237-46,523,659

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