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: Write down all possible factors for 3a^2b. To find all factors, we consider the numerical factors of 3 and the variable factors of a^2b. The prime factorization of 3a^2b is 3 × a × a × b. The factors are: 1, 3, a, b, a^2, 3a, 3b, ab, a^2b, 3a^2, 3ab, 3a^2b Step 2: Write down all possible factors for 4ab^2. To find all factors, we consider the numerical factors of 4 and the variable factors of ab^2. The prime factorization of 4ab^2 is 2 × 2 × a × b × b. The factors are: 1, 2, 4, a, b, b^2, 2a, 2b, 2b^2, 4a, 4b, 4b^2, ab, ab^2, 2ab, 2ab^2, 4ab, 4ab^2 Step 3: Determine the H.C.F. of 3a^2b and 4ab^2. To find the Highest Common Factor (H.C.F.), we find the H.C.F. of the numerical coefficients and the variable parts separately. • Numerical coefficients: The factors of 3 are \1, 3\. The factors of 4 are \1, 2, 4\. The H.C.F. of 3 and 4 is 1. • Variable parts: For a^2b and ab^2: • For the variable a: The lowest power of a present in both terms is a^1. • For the variable b: The lowest power of b present in both terms is b^1. Combining these, the H.C.F. of the variable parts is ab. Therefore, the H.C.F. of 3a^2b and 4ab^2 is 1 × ab = ab. The H.C.F. of the algebraic expression is ab. Send me the next one 📸