**The prime factorization of 160 can be given as 2 x 2 x 2 x 2 x 2 x 5; it can also be expressed using exponents as 2 ^{5} x 5.** The prime factorization of a number is finding the prime factors that, when multiplied together, produce this number.

The method used to perform prime factorization for numbers is to divide the given number by prime numbers until all prime factors are found. The process entails successive divisions and often requires starting this division process with the smallest prime number. For example, the number 160 is divisible by the smallest prime number, which is 2. This division is given as 160 = 2 x 80. The number 80 is then divided by 2 again and the factorization becomes 160 = 2 x 2 x 40. This process is repeated until the result is 160 = 2 x 2 x 2 x 2 x 2 x 5. Exponential form is useful to express prime factorization and avoid having to write out all the prime factors.

Performing these calculations to find prime factors of a number by hand can be tedious and long, especially when the number given is a large number. However, there are prime factorization calculators that can help with these calculations and confirm that the solution is correct.