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.
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Another one ameyawaugustine10@gmail.c — let's solve it. 1. Find the HCF of 43, 91 and 183. Step 1: Find the prime factorization of each number. 43 = 43 (43 is a prime number) 91 = 7 × 13 183 = 3 × 61 Step 2: Identify common prime factors. The numbers 43, 91, and 183 have no common prime factors other than 1. Step 3: The HCF is the product of the common prime factors. Since there are no common prime factors other than 1, the HCF is 1. HCF(43, 91, 183) = 1 The HCF of 43, 91, and 183 is 1. 2. What is the LCM of 24, 36 and 40? Step 1: Find the prime factorization of each number. 24 = 2 × 2 × 2 × 3 = 2^3 × 3^1 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2 40 = 2 × 2 × 2 × 5 = 2^3 × 5^1 Step 2: For each prime factor, take the highest power that appears in any of the factorizations. • For prime factor 2: The highest power is 2^3 (from 24 and 40). • For prime factor 3: The highest power is 3^2 (from 36). • For prime factor 5: The highest power is 5^1 (from 40). Step 3: Multiply these highest powers to find the LCM. LCM(24, 36, 40) = 2^3 × 3^2 × 5^1 LCM(24, 36, 40) = 8 × 9 × 5 LCM(24, 36, 40) = 72 × 5 LCM(24, 36, 40) = 360 The LCM of 24, 36, and 40 is 360. 3. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one number is 275, then find the other number. Step 1: Use the relationship between HCF, LCM, and the product of two numbers. For any two positive integers a and b: a × b = HCF(a, b) × LCM(a, b) Step 2: Substitute the given values into the formula. Let the first number be a = 275. Let the second number be b. Given HCF = 11. Given LCM = 7700. 275 × b = 11 × 7700 Step 3: Solve for b. 275 × b = 84700 b = (84700)/(275) b = 308 The other number is 308. 4. List 5 pairs of relative numbers. Relative numbers (also known as coprime or relatively prime numbers) are two integers whose greatest common divisor (HCF) is 1. Here are 5 pairs of relative numbers: • (2, 3) • (4, 5) • (7, 10) • (9, 16) • (15, 22) Send me the next one 📸