Q: What are the factor combinations of the number 53,521,721?

 A:
Positive:   1 x 5352172111 x 486561137 x 1446533107 x 500203407 x 1315031177 x 454731229 x 435493959 x 13519
Negative: -1 x -53521721-11 x -4865611-37 x -1446533-107 x -500203-407 x -131503-1177 x -45473-1229 x -43549-3959 x -13519


How do I find the factor combinations of the number 53,521,721?

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 53,521,721, 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 53,521,721
-1 -53,521,721

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 53,521,721.

Example:
1 x 53,521,721 = 53,521,721
and
-1 x -53,521,721 = 53,521,721
Notice both answers equal 53,521,721

With that explanation out of the way, let's continue. Next, we take the number 53,521,721 and divide it by 2:

53,521,721 ÷ 2 = 26,760,860.5

If the quotient is a whole number, then 2 and 26,760,860.5 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 53,521,721
-1 -53,521,721

Now, we try dividing 53,521,721 by 3:

53,521,721 ÷ 3 = 17,840,573.6667

If the quotient is a whole number, then 3 and 17,840,573.6667 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 53,521,721
-1 -53,521,721

Let's try dividing by 4:

53,521,721 ÷ 4 = 13,380,430.25

If the quotient is a whole number, then 4 and 13,380,430.25 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 53,521,721
-1 53,521,721
Keep dividing by the next highest number until you cannot divide anymore.

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

111371074071,1771,2293,95913,51943,54945,473131,503500,2031,446,5334,865,61153,521,721
-1-11-37-107-407-1,177-1,229-3,959-13,519-43,549-45,473-131,503-500,203-1,446,533-4,865,611-53,521,721

More Examples

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