This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: List the numbers: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. A prime number has no positive divisors other than 1 and itself. Check each number for divisibility by primes up to its square root. Step 2: Check 20. sqrt(20) ≈ 4.47, test primes: 2, 3. 20 ÷ 2 = 10 (integer). Not prime. Step 3: Check 21. sqrt(21) ≈ 4.58, test primes: 2, 3. Sum of digits: 2+1=3, divisible by 3. 21 ÷ 3 = 7 (integer). Not prime. Step 4: Check 22. sqrt(22) ≈ 4.69, test primes: 2, 3. 22 ÷ 2 = 11 (integer). Not prime. Step 5: Check 23. sqrt(23) ≈ 4.80, test primes: 2, 3. Odd, not divisible by 2. Sum of digits: 2+3=5, not divisible by 3. Prime. Step 6: Check 24. Even and greater than 2. 24 ÷ 2 = 12 (integer). Not prime. Step 7: Check 25. sqrt(25) = 5, test primes: 2, 3, 5. Ends in 5. 25 ÷ 5 = 5 (integer). Not prime. Step 8: Check 26. Even and greater than 2. 26 ÷ 2 = 13 (integer). Not prime. Step 9: Check 27. sqrt(27) ≈ 5.20, test primes: 2, 3, 5. Sum of digits: 2+7=9, divisible by 3. 27 ÷ 3 = 9 (integer). Not prime. Step 10: Check 28. Even and greater than 2. 28 ÷ 2 = 14 (integer). Not prime. Step 11: Check 29. sqrt(29) ≈ 5.39, test primes: 2, 3, 5. Odd, not divisible by 2. Sum of digits: 2+9=11, not divisible by 3. Does not end in 0 or 5, not divisible by 5. Prime. Step 12: Check 30. Even and ends in 0. 30 ÷ 2 = 15 (integer). Not prime. The prime numbers are 23 and 29. 23, 29