Real Numbers · Class 10 · CBSE Mathematics

Let a and b be two positive integers such that a = x^3 y^2 and b = x y^3, where x and y are prime numbers. What is text{HCF}(a, b)?

Practice question from Real Numbers (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-8C7F18

Let $a$ and $b$ be two positive integers such that $a = x^3 y^2$ and $b = x y^3$ , where $x$ and $y$ are prime numbers. What is $\text{HCF}(a, b)$ ?

A. $x^3 y^3$
B. $x y$
C. $x y^2$ Correct answer
D. $x^2 y^2$

Solution

Given $a = x^3 y^2$ and $b = x y^3$ . The HCF is found by taking the lowest power of common prime factors $x$ and $y$ . The lowest power of $x$ is $x^1$ and of $y$ is $y^2$ . Therefore, $\text{HCF}(a, b) = xy^2$ .

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