Q: What are the factor combinations of the number 30,224,225?

 A:
Positive:   1 x 302242255 x 604484525 x 120896931 x 97497559 x 512275155 x 194995295 x 102455661 x 45725775 x 389991475 x 204911829 x 165253305 x 9145
Negative: -1 x -30224225-5 x -6044845-25 x -1208969-31 x -974975-59 x -512275-155 x -194995-295 x -102455-661 x -45725-775 x -38999-1475 x -20491-1829 x -16525-3305 x -9145


How do I find the factor combinations of the number 30,224,225?

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 30,224,225, 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 30,224,225
-1 -30,224,225

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 30,224,225.

Example:
1 x 30,224,225 = 30,224,225
and
-1 x -30,224,225 = 30,224,225
Notice both answers equal 30,224,225

With that explanation out of the way, let's continue. Next, we take the number 30,224,225 and divide it by 2:

30,224,225 ÷ 2 = 15,112,112.5

If the quotient is a whole number, then 2 and 15,112,112.5 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 30,224,225
-1 -30,224,225

Now, we try dividing 30,224,225 by 3:

30,224,225 ÷ 3 = 10,074,741.6667

If the quotient is a whole number, then 3 and 10,074,741.6667 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 30,224,225
-1 -30,224,225

Let's try dividing by 4:

30,224,225 ÷ 4 = 7,556,056.25

If the quotient is a whole number, then 4 and 7,556,056.25 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 30,224,225
-1 30,224,225
Keep dividing by the next highest number until you cannot divide anymore.

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

152531591552956617751,4751,8293,3059,14516,52520,49138,99945,725102,455194,995512,275974,9751,208,9696,044,84530,224,225
-1-5-25-31-59-155-295-661-775-1,475-1,829-3,305-9,145-16,525-20,491-38,999-45,725-102,455-194,995-512,275-974,975-1,208,969-6,044,845-30,224,225

More Examples

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