Q: What are the factor combinations of the number 12,224,225?

 A:
Positive:   1 x 122242255 x 244484513 x 94032525 x 48896929 x 42152565 x 188065145 x 84305325 x 37613377 x 32425725 x 168611297 x 94251885 x 6485
Negative: -1 x -12224225-5 x -2444845-13 x -940325-25 x -488969-29 x -421525-65 x -188065-145 x -84305-325 x -37613-377 x -32425-725 x -16861-1297 x -9425-1885 x -6485


How do I find the factor combinations of the number 12,224,225?

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 12,224,225, 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 12,224,225
-1 -12,224,225

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 12,224,225.

Example:
1 x 12,224,225 = 12,224,225
and
-1 x -12,224,225 = 12,224,225
Notice both answers equal 12,224,225

With that explanation out of the way, let's continue. Next, we take the number 12,224,225 and divide it by 2:

12,224,225 ÷ 2 = 6,112,112.5

If the quotient is a whole number, then 2 and 6,112,112.5 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 12,224,225
-1 -12,224,225

Now, we try dividing 12,224,225 by 3:

12,224,225 ÷ 3 = 4,074,741.6667

If the quotient is a whole number, then 3 and 4,074,741.6667 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 12,224,225
-1 -12,224,225

Let's try dividing by 4:

12,224,225 ÷ 4 = 3,056,056.25

If the quotient is a whole number, then 4 and 3,056,056.25 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 12,224,225
-1 12,224,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15132529651453253777251,2971,8856,4859,42516,86132,42537,61384,305188,065421,525488,969940,3252,444,84512,224,225
-1-5-13-25-29-65-145-325-377-725-1,297-1,885-6,485-9,425-16,861-32,425-37,613-84,305-188,065-421,525-488,969-940,325-2,444,845-12,224,225

More Examples

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