Question 1 What is a composite number between 20 and 40? Answer 1 A composite number is a number that has factors other than 1 and itself. The composite numbers between 20 and 40 are: 20 = 2 × 2 × 5 2×2×5 21 = 3 × 7 3×7 24 = 2 × 2 × 2 × 3 2×2×2×3 25 = 5 × 5 5×5 26 = 2 × 13 2×13 27 = 3 × 3 × 3 3×3×3 28 = 2 × 2 × 7 2×2×7 30 = 2 × 3 × 5 2×3×5 32 = 2 × 2 × 2 × 2 × 2 2×2×2×2×2 33 = 3 × 11 3×11 34 = 2 × 17 2×17 35 = 5 × 7 5×7 36 = 2 × 2 × 3 × 3 2×2×3×3 38 = 2 × 19 2×19 39 = 3 × 13 3×13 40 = 2 × 2 × 2 × 5 2×2×2×5 The prime numbers between 20 and 40 (not composite) are: 23, 29, 31, 37. Question 2 Is 69 a prime number? Answer 1 No, 69 is a composite number. Explanation: 69 is divisible by 3. 69 = 3 × 23 69=3×23 Since 69 has a factor of 3 other than 1 and itself, it is not a prime number. Question 3 How do you write the factorization of − 38 𝑚 𝑛 𝑝 −38mnp? Answer 1 The prime factorization of − 38 𝑚 𝑛 𝑝 −38mnp: − 38 𝑚 𝑛 𝑝 = − 1 × 2 × 19 × 𝑚 × 𝑛 × 𝑝 −38mnp=−1×2×19×m×n×p Here, -1 is included to indicate the sign, and 2 2 and 19 19 are prime factors of 38. Question 4 What is the factorization of 86? Answer 1 The factorization of 86 is: 86 = 2 × 43 86=2×43 Explanation: 86 ends with an even digit, so it is divisible by 2. Dividing by 2 gives 43, which is a prime number. Question 5 How do you write the factorization of − 75 𝑎 𝑏 2 −75ab 2 ? Answer 1 The factorization of − 75 𝑎 𝑏 2 −75ab 2 : Factor out 75 as 5 × 5 × 3 5×5×3. Include the variable terms 𝑎 a and 𝑏 2 b 2 . Result: − 75 𝑎 𝑏 2 = − 1 × 3 × 5 2 × 𝑎 × 𝑏 2 −75ab 2 =−1×3×5 2 ×a×b 2