Q: What are the factor combinations of the number 23,320,225?

 A:
Positive:   1 x 233202255 x 466404525 x 93280947 x 49617589 x 262025223 x 104575235 x 99235445 x 524051115 x 209151175 x 198472225 x 104814183 x 5575
Negative: -1 x -23320225-5 x -4664045-25 x -932809-47 x -496175-89 x -262025-223 x -104575-235 x -99235-445 x -52405-1115 x -20915-1175 x -19847-2225 x -10481-4183 x -5575


How do I find the factor combinations of the number 23,320,225?

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 23,320,225, 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 23,320,225
-1 -23,320,225

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 23,320,225.

Example:
1 x 23,320,225 = 23,320,225
and
-1 x -23,320,225 = 23,320,225
Notice both answers equal 23,320,225

With that explanation out of the way, let's continue. Next, we take the number 23,320,225 and divide it by 2:

23,320,225 ÷ 2 = 11,660,112.5

If the quotient is a whole number, then 2 and 11,660,112.5 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 23,320,225
-1 -23,320,225

Now, we try dividing 23,320,225 by 3:

23,320,225 ÷ 3 = 7,773,408.3333

If the quotient is a whole number, then 3 and 7,773,408.3333 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 23,320,225
-1 -23,320,225

Let's try dividing by 4:

23,320,225 ÷ 4 = 5,830,056.25

If the quotient is a whole number, then 4 and 5,830,056.25 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 23,320,225
-1 23,320,225
Keep dividing by the next highest number until you cannot divide anymore.

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

152547892232354451,1151,1752,2254,1835,57510,48119,84720,91552,40599,235104,575262,025496,175932,8094,664,04523,320,225
-1-5-25-47-89-223-235-445-1,115-1,175-2,225-4,183-5,575-10,481-19,847-20,915-52,405-99,235-104,575-262,025-496,175-932,809-4,664,045-23,320,225

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