Find the prime factorization of the number 84.One of the prime factors is missing from the following list:2, 2, 3What is the missing prime factor?

To find the missing prime factor of the number 84, we'll follow these steps:

1. Break Down the Problem

We need to determine the complete prime factorization of the number 84 and identify the missing prime factor from the provided list $\{2, 2, 3\}$.

2. Relevant Concepts

The prime factorization of a number is the expression of that number as a product of prime numbers. The methods usually employed include division by prime numbers.

3. Analysis and Detail

We'll find the prime factorization of 84:

1. Start with the smallest prime number, which is 2: $84 \div 2 = 42$

2. Continue dividing by 2: $42 \div 2 = 21$ So we have $2 \times 2$ so far.

3. Now, we will move to the next smallest prime number, which is 3: $21 \div 3 = 7$ Now we have $2 \times 2 \times 3$.

4. The remaining number 7 is also a prime number.

Putting this all together, the complete prime factorization of 84 is: $84 = 2^2 \times 3 \times 7$

4. Verify and Summarize

From our calculations, we found the prime factorization to be $2^2 \times 3 \times 7$. The list provided was $\{2, 2, 3\}$. Therefore, the missing prime factor is:

Final Answer

The missing prime factor is 7.