Here is the code :

Python:

```
def prime_factors(number):
factors = []
for i in range(2, number + 1):
while number % i == 0:
factors.append(i)
number = number / i
return factors
print("Prime factorization of 60:", prime_factors(60))
```

This challenge requires a good understanding of loops, control flow, data structures, and mathematical concepts such as prime numbers and factorization. Good luck!