Prime factorization is a mathematical process used to break down a number into its prime numbers. In other words, it is the process of finding which prime numbers multiplied together equal the original number. For example, the prime factorization of 729 is 3 x 3 x 3 x 3 x 3.

How to Find the Prime Factors of 729?

To find the prime factors of 729, we must first identify the prime numbers that are factors of 729. The prime numbers that are factors of 729 are 3, 7, and 11. We can then use these prime numbers to break down 729 into its prime factors.

Step 1: Divide the Number by the Smallest Prime Number

The first step in finding the prime factorization of 729 is to divide it by the smallest prime number, which in this case is 3. When we divide 729 by 3, we get 243.

Step 2: Divide the Result by the Same Prime Number

The next step is to divide the result of the first step, 243, by the same prime number, 3. When we divide 243 by 3, we get 81.

Step 3: Divide the Result by the Same Prime Number

The next step is to divide the result of the second step, 81, by the same prime number, 3. When we divide 81 by 3, we get 27.

Step 4: Divide the Result by the Same Prime Number

The next step is to divide the result of the third step, 27, by the same prime number, 3. When we divide 27 by 3, we get 9.

Step 5: Divide the Result by the Same Prime Number

The next step is to divide the result of the fourth step, 9, by the same prime number, 3. When we divide 9 by 3, we get 3.

Step 6: Check to See if the Result is a Prime Number

The last step is to check to see if the result of the fifth step, 3, is a prime number. Since 3 is a prime number, we have found the prime factorization of 729.

Conclusion

The prime factorization of 729 is 3 x 3 x 3 x 3 x 3. This can be found by dividing 729 by the smallest prime number, which is 3, and then repeating the process until the result is a prime number. Knowing the prime factorization of a number can be useful in solving certain types of mathematical problems.