NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 6

Question.  6

If two positive integers a and b are written as \(a = x^3y^2\) and \(b = xy^3\); \(x, y\) are prime numbers, then \(HCF(a, b)\) is

(A)

\(xy\)

(B)

\(xy^2\)

(C)

\(x^3y^3\)

(D)

\(x^2y^2\)

Handwritten Notes

If two positive integers a and b are written as \(a = x^3y^2\) and \(b = xy^3\); \(x, y\) are prime numbers, then \(HCF(a, b)\) is 1
If two positive integers a and b are written as \(a = x^3y^2\) and \(b = xy^3\); \(x, y\) are prime numbers, then \(HCF(a, b)\) is 2
If two positive integers a and b are written as \(a = x^3y^2\) and \(b = xy^3\); \(x, y\) are prime numbers, then \(HCF(a, b)\) is 3

Video Explanation:

Detailed Answer with Explanation:

The HCF is found by taking the smallest power of each prime factor in both numbers.

For \(x\), the powers are \(3\) (in a) and \(1\) (in b). The minimum is \(1\).

For \(y\), the powers are \(2\) (in a) and \(3\) (in b). The minimum is \(2\).

So, the HCF is \(x^1y^2 = xy^2\).

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NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 1: Real Numbers – Exercise 1.1 - Multiple Choice Questions | Detailed Answers