Find the prime factorization of 120.

Divide 120 by the smallest prime number, 2.

Divide 60 by 2.

Divide 30 by 2.

Now, 15 is not divisible by 2. Divide 15 by the next smallest prime number, 3.

Now, 5 is not divisible by 3. Divide 5 by the next smallest prime number, 5.

The prime factors of 120 are $2, 2, 2, 3, 5$.

Count the occurrences of each prime factor:
The prime factor 2 appears 3 times, so it can be written as $2^3$.
The prime factor 3 appears 1 time, so it can be written as $3^1$ or simply 3.
The prime factor 5 appears 1 time, so it can be written as $5^1$ or simply 5.

The prime factorization of 120 is $\boxed{2^3 \times 3 \times 5}$.