Q: What are the factor combinations of the number 52,215,221?

 A:
Positive:   1 x 5221522123 x 227022773 x 715277137 x 381133227 x 2300231679 x 310993151 x 165715221 x 10001
Negative: -1 x -52215221-23 x -2270227-73 x -715277-137 x -381133-227 x -230023-1679 x -31099-3151 x -16571-5221 x -10001


How do I find the factor combinations of the number 52,215,221?

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 52,215,221, 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 52,215,221
-1 -52,215,221

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 52,215,221.

Example:
1 x 52,215,221 = 52,215,221
and
-1 x -52,215,221 = 52,215,221
Notice both answers equal 52,215,221

With that explanation out of the way, let's continue. Next, we take the number 52,215,221 and divide it by 2:

52,215,221 ÷ 2 = 26,107,610.5

If the quotient is a whole number, then 2 and 26,107,610.5 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 52,215,221
-1 -52,215,221

Now, we try dividing 52,215,221 by 3:

52,215,221 ÷ 3 = 17,405,073.6667

If the quotient is a whole number, then 3 and 17,405,073.6667 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 52,215,221
-1 -52,215,221

Let's try dividing by 4:

52,215,221 ÷ 4 = 13,053,805.25

If the quotient is a whole number, then 4 and 13,053,805.25 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 52,215,221
-1 52,215,221
Keep dividing by the next highest number until you cannot divide anymore.

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

123731372271,6793,1515,22110,00116,57131,099230,023381,133715,2772,270,22752,215,221
-1-23-73-137-227-1,679-3,151-5,221-10,001-16,571-31,099-230,023-381,133-715,277-2,270,227-52,215,221

More Examples

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