The prime factorization of 201 is 3 x 67.
To arrive at this conclusion, we first need to determine if 201 is divisible by the smallest prime numbers. Starting with 2, we see that 201 is odd and therefore not divisible by 2. Next, we check 3 by adding the digits of 201 (2 + 0 + 1 = 3), which is divisible by 3. Dividing 201 by 3 gives us 67.
Now we need to test if 67 is a prime number. It is not divisible by 2, 3, 5, or 7, confirming that there are no factors other than 1 and 67 itself. Thus, 67 is indeed a prime number.
Combining these results, we conclude that the prime factorization of 201 is 3 and 67.