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
Here's how to factorize the pairs of numbers, find the product of their common prime factors (HCF), and test if it divides the given numbers. a) 8 and 12 Step 1: Find the prime factors of 8 and 12. 8 = 2 × 2 × 2 12 = 2 × 2 × 3 Step 2: Identify the common prime factors and calculate their product (HCF). The common prime factors are 2 × 2 = 4. Step 3: Test if the product (4) exactly divides 8 and 12. 8 ÷ 4 = 2 12 ÷ 4 = 3 Both divisions are exact. HCF = 4, Yes, it divides both numbers. b) 18 and 24 Step 1: Find the prime factors of 18 and 24. 18 = 2 × 3 × 3 24 = 2 × 2 × 2 × 3 Step 2: Identify the common prime factors and calculate their product (HCF). The common prime factors are 2 × 3 = 6. Step 3: Test if the product (6) exactly divides 18 and 24. 18 ÷ 6 = 3 24 ÷ 6 = 4 Both divisions are exact. HCF = 6, Yes, it divides both numbers. c) 20 and 30 Step 1: Find the prime factors of 20 and 30. 20 = 2 × 2 × 5 30 = 2 × 3 × 5 Step 2: Identify the common prime factors and calculate their product (HCF). The common prime factors are 2 × 5 = 10. Step 3: Test if the product (10) exactly divides 20 and 30. 20 ÷ 10 = 2 30 ÷ 10 = 3 Both divisions are exact. HCF = 10, Yes, it divides both numbers. d) 36 and 48 Step 1: Find the prime factors of 36 and 48. 36 = 2 × 2 × 3 × 3 48 = 2 × 2 × 2 × 2 × 3 Step 2: Identify the common prime factors and calculate their product (HCF). The common prime factors are 2 × 2 × 3 = 12. Step 3: Test if the product (12) exactly divides 36 and 48. 36 ÷ 12 = 3 48 ÷ 12 = 4 Both divisions are exact. HCF = 12, Yes, it divides both numbers. That's 2 down. 3 left today — send the next one.