CTET Paper II (Mathematics and Science) Jul 2019 Solved Paper

Concept:HCF is the product of the smallest exponent of each common prime factor among the numbers.Explanation:For each prime, take the lowest power from x, y, and z.For 2: exponents 3, 2, 4 → lowest is 2 → $2^2$.For 3: exponents 2, 3, 4 → lowest is 2 → $3^2$.For 5: exponents 3, 4, 2 → lowest is 2 → $5^2$.For 7: exponents 3, 3, 5 → lowest is 3 → $7^3$.Multiply: HCF = $2^2 \times 3^2 \times 5^2 \times 7^3 = (2 \times 3 \times 5)^2 \times 7^3 = 30^2 \times 7^3$.Answer:D. $(30)^{2} \times 7^{3}$