The prime factorization of a number can be achieved by breaking down the number into its prime factors. This is an essential concept in maths, and understanding it is crucial for solving various problems. In this post, we will be discussing the prime factorization of 48.

The first step in finding the prime factorization of 48 is to divide it by the smallest prime number possible, which is 2. When you divide 48 by 2, you get 24. Since 24 is also divisible by 2, divide it again by 2, and you get 12. Continuing this process, you will find that 12 can also be divided by 2, giving you 6. And again, 6 can be divided by 2, giving you 3.

At this point, we have reached a prime number (3), meaning there is nowhere else to go with our division process. Therefore, the prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 2^4 x 3.

To check if this factorization is correct, you can multiply the primes back together: 2 x 2 x 2 x 2 x 3 = 48.

Another way to find the prime factorization of a number is to use a factor tree. Here’s how it would look for 48:

48

/ \

2 24

/ \

2 12

/ \

2 6

/ \

2 3

As you can see, we start by dividing 48 by 2 to get 24, then continue to break down the factors until we reach only primes.

In conclusion, the prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 2^4 x 3. Remember, this process can be applied to any number, and it is an essential tool for solving various maths problems.