Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding stimulus
Model Answer
First, find the prime factorisation of 173250:
173250 = 2 × 86625 = 2 × 3 × 28875 = 2 × 3 × 3 × 9625 = 2 × 3 × 3 × 5 × 1925 = 2 × 3 × 3 × 5 × 5 × 385 = 2 × 3 × 3 × 5 × 5 × 5 × 77 = 2 × 3 × 3 × 5 × 5 × 5 × 7 × 11
So, 173250 = 2 × 3² × 5³ × 7 × 11
The game starts with 2 (announced by Ms. Mukta), so students multiply by the remaining prime factors: 3, 3, 5, 5, 5, 7, 11.
(i) The least prime number used by students = 3
(2 was the starting number announced by the teacher, not multiplied by a student.)
(ii) The prime factors multiplied by students are: 3, 3, 5, 5, 5, 7, 11 → 7 students are in the class.
(iii) 5 appears 3 times, which is the maximum. The prime number used maximum times = 5.
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Explanation
- Start with prime factorisation of 173250 — this is the key step.
- Since Ms. Mukta announced 2 (she didn't multiply), students only multiply the remaining factors. Count those factors = number of students.
- "Least prime used by students" excludes 2 (the teacher's starting number), so the answer is 3, not 2. Some students miss this nuance — read the passage carefully.
- "Maximum times" means the factor with the highest frequency → 5 (appears 3 times).