The prime factorization of 99 is 3² × 11.
To explain how we arrive at this, we start by finding the prime numbers that multiply together to give 99. We begin by testing the smallest prime number, which is 2. Since 99 is an odd number, it is not divisible by 2. Next, we try 3. Dividing 99 by 3 gives us 33, which means 3 is a factor.
Continuing with 33, we again check for prime factors. 33 is divisible by 3 (33 ÷ 3 = 11). Now we have found that:
- 99 = 3 × 33
- 33 = 3 × 11
Thus, we can express 99 as:
99 = 3 × 3 × 11
Since there are two occurrences of the prime number 3, we can write it using exponents: 3². Therefore, the complete prime factorization of 99 is:
3² × 11.