Q: What are the factor combinations of the number 49,085,729?

 A:
Positive:   1 x 490857297 x 701224711 x 446233977 x 637477443 x 1108031439 x 341113101 x 158294873 x 10073
Negative: -1 x -49085729-7 x -7012247-11 x -4462339-77 x -637477-443 x -110803-1439 x -34111-3101 x -15829-4873 x -10073


How do I find the factor combinations of the number 49,085,729?

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 49,085,729, 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 49,085,729
-1 -49,085,729

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 49,085,729.

Example:
1 x 49,085,729 = 49,085,729
and
-1 x -49,085,729 = 49,085,729
Notice both answers equal 49,085,729

With that explanation out of the way, let's continue. Next, we take the number 49,085,729 and divide it by 2:

49,085,729 ÷ 2 = 24,542,864.5

If the quotient is a whole number, then 2 and 24,542,864.5 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 49,085,729
-1 -49,085,729

Now, we try dividing 49,085,729 by 3:

49,085,729 ÷ 3 = 16,361,909.6667

If the quotient is a whole number, then 3 and 16,361,909.6667 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 49,085,729
-1 -49,085,729

Let's try dividing by 4:

49,085,729 ÷ 4 = 12,271,432.25

If the quotient is a whole number, then 4 and 12,271,432.25 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 49,085,729
-1 49,085,729
Keep dividing by the next highest number until you cannot divide anymore.

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

1711774431,4393,1014,87310,07315,82934,111110,803637,4774,462,3397,012,24749,085,729
-1-7-11-77-443-1,439-3,101-4,873-10,073-15,829-34,111-110,803-637,477-4,462,339-7,012,247-49,085,729

More Examples

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