Find the prime factorization of the number 280.One of the prime factors is missing from the following list:2, 2, 2, 5What is the missing prime factor?

To find the missing prime factor of the number 280 when given part of its prime factorization, we can follow these steps:

1. Break Down the Problem

The goal is to find the complete prime factorization of 280 and identify any missing factors from the provided list.

2. Relevant Concepts

Prime factorization involves breaking down a number into its prime factors. The number 280 can be factorized step by step using division by prime numbers.

3. Analysis and Detail

1. Start with the number 280.
2. Divide by the smallest prime number, which is 2: $280 \div 2 = 140$
3. Divide 140 by 2: $140 \div 2 = 70$
4. Divide 70 by 2: $70 \div 2 = 35$
5. Now, 35 is not divisible by 2. The next prime number is 5: $35 \div 5 = 7$
6. Finally, we are left with 7, which is also a prime number.

This gives us: $280 = 2 \times 2 \times 2 \times 5 \times 7$

4. Verify and Summarize

The full prime factorization of 280 is: $280 = 2^3 \times 5 \times 7$ From the provided list, we have identified that the missing prime factor is 7.

Final Answer

The missing prime factor is 7.