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Prime factorization is the process of expressing a positive integer greater than 1 as the product of its prime factors. In other words, it involves finding the prime numbers that, when multiplied together, give the original number. Prime factorization is a fundamental concept in number theory and has various applications in mathematics and computer science.

To find the prime factorization of a number, you can follow these steps:

Start with the smallest prime number, which is 2.

Divide the given number by 2 and continue dividing until it is no longer divisible by 2. Keep track of how many times it is divisible by 2.

Move to the next prime number, which is 3, and repeat the division process until the number is no longer divisible by 3. Again, keep track of the number of divisions.

Continue this process with the next prime numbers: 5, 7, 11, 13, 17, 19, and so on. Divide the number by each prime until it is no longer divisible.

Repeat steps 2 to 4 until the number becomes 1.

The prime factors obtained from this process, including their multiplicities (how many times they divide the original number), give the prime factorization of the original number.

For example, let’s find the prime factorization of 84:

Start with the smallest prime, 2. Divide 84 by 2, which gives 42. Dividing 42 by 2 again, we get 21.

Now, move to the next prime, 3. Dividing 21 by 3, we get 7.

The number 7 is a prime number itself, so we stop here.

The prime factors are 2, 2, 3, and 7. Multiplying them together: 2 x 2 x 3 x 7 = 84. Therefore, the prime factorization of 84 is 2^2 x 3 x 7.

It’s worth noting that if the given number is prime itself, its prime factorization would simply be the number itself raised to the power of 1.