4. Find a common prime fac a) 21 and 411

To find the common prime factors of 21 and 411, we will first determine the prime factorization of each number. ### Step 1: Prime Factorization of 21 The number 21 can be factored as follows: - 21 is divisible by 3 (since \(21 \div 3 = 7\)). - Both 3 and 7 are prime numbers. Thus, the prime factorization of 21 is: \[ 21 = 3 \times 7 \] ### Step 2: Prime Factorization of 411 Next, we will factor 411: - 411 is divisible by 3 (since \(411 \div 3 = 137\)). - Now, we need to check if 137 is a prime number. It is not divisible by 2, 3, 5, 7, 11, or 13, which means 137 is a prime number. Thus, the prime factorization of 411 is: \[ 411 = 3 \times 137 \] ### Step 3: Identify Common Prime Factors Now we can compare the prime factorizations: - Prime factors of 21: \(3, 7\) - Prime factors of 411: \(3, 137\) The common prime factor between 21 and 411 is: \[ \text{Common Prime Factor} = 3 \] ### Conclusion The common prime factor of 21 and 411 is \(3\).