To find the prime factorization of 484, we need to break it down into its smallest prime factors.
1. Start by dividing 484 by the smallest prime number, which is 2.
484 ÷ 2 = 242
2. Next, we can divide 242 by 2 again.
242 ÷ 2 = 121
3. Now, we need to factor 121. Since 121 is not divisible by 2, we check the next prime number, which is 3. It’s also not divisible by 3. Next, we try 5, and then 7, but 121 is not divisible by any of these. When we try 11, we find:
121 ÷ 11 = 11
4. Since 11 is a prime number, we can stop here.
Putting it all together, we have:
484 = 2 × 2 × 11 × 11
Which can also be written as:
484 = 22 × 112
So, the prime factorization of 484 is 22 × 112.