To find the prime factorization of 363, we start by dividing the number by the smallest prime number, which is 2. Since 363 is odd, it cannot be divided by 2. Next, we check 3.
When we divide 363 by 3, we get:
363 ÷ 3 = 121
Now we need to factor 121. We can again start with the smallest primes. It’s not divisible by 2 or 3, but when we check 11:
121 ÷ 11 = 11
Since 11 is a prime number, we stop here. Thus, the complete factorization is:
363 = 3 × 11 × 11
To express this in exponential form, we can write:
363 = 3 × 112
In conclusion, the prime factorization of 363 is 3 × 112.