Q: What are the factor combinations of the number 72,767,233?

 A:
Positive:   1 x 727672337 x 1039531911 x 661520347 x 154823977 x 945029329 x 221177517 x 1407493619 x 20107
Negative: -1 x -72767233-7 x -10395319-11 x -6615203-47 x -1548239-77 x -945029-329 x -221177-517 x -140749-3619 x -20107


How do I find the factor combinations of the number 72,767,233?

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 72,767,233, 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 72,767,233
-1 -72,767,233

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 72,767,233.

Example:
1 x 72,767,233 = 72,767,233
and
-1 x -72,767,233 = 72,767,233
Notice both answers equal 72,767,233

With that explanation out of the way, let's continue. Next, we take the number 72,767,233 and divide it by 2:

72,767,233 ÷ 2 = 36,383,616.5

If the quotient is a whole number, then 2 and 36,383,616.5 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 72,767,233
-1 -72,767,233

Now, we try dividing 72,767,233 by 3:

72,767,233 ÷ 3 = 24,255,744.3333

If the quotient is a whole number, then 3 and 24,255,744.3333 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 72,767,233
-1 -72,767,233

Let's try dividing by 4:

72,767,233 ÷ 4 = 18,191,808.25

If the quotient is a whole number, then 4 and 18,191,808.25 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 72,767,233
-1 72,767,233
Keep dividing by the next highest number until you cannot divide anymore.

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

171147773295173,61920,107140,749221,177945,0291,548,2396,615,20310,395,31972,767,233
-1-7-11-47-77-329-517-3,619-20,107-140,749-221,177-945,029-1,548,239-6,615,203-10,395,319-72,767,233

More Examples

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