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Piyush365
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Asked: 2026-09-29T06:24:26+00:00 In:

If n is the square of a prime number, then it has exactly 3 factors (where n is a positive integer).

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Both the proposition and its converse (“If n has exactly 3 factors, then it is the square of a prime number”) are true, with factors being 1, p and p².

Class 9 Ganita Manjari Part II Propositions and their Converses Solutions
Class 9 Ganita Manjari Part 2 chapter 9 Propositions and their Converses solutions

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    1. Both the proposition and its converse (“If n has exactly 3 factors, then it is the square of a prime number”) are true. If n = p² for a prime p, its only divisors are 1, p and p². Conversely, a number with an odd factor count is a perfect square and having exactly 3 factors forces its prime factorization to be p².

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/

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