**Q)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.**

**Now, Mukta asked some questions as given below to the students :(i) What is the least prime number used by students?(ii) (a) How many students are in the class?OR(b) What is the highest prime number used by students?(iii) Which prime number has been used maximum times?**

**Ans: **

Since Each student multiplies by a prime number, they got final number as 73250.

It means 173250 is the product of all the prime numbers chosen by each student.

Therefore, if we do the prime factorisation of 173250 , we will get the construct of it.

Hence, by prime factorisation, we get:

173250 = 2 x 5 x 5 x 5 x 3 x 3 x 7 x 11

**(i) Least prime number:**

From the prime factorisation, we note that prime numbers used are 2, 3, 5, 7 and 11. In these prime numbers, 2 is the smallest prime number of all.

**Therefore, the least prime number used by students is 2.**

**(ii) (a) Number of students:**

Number of students in the class = number of prime numbers used to reach 173250

Since prime numbers used in total = 8

**Therefore, there are 8 students in the class.**

**OR(b) Highest prime number:**

As we can see the prime factorisation, we note that 11 is the largest prime number

**Therefore, highest prime number used by students is 11.**

**(iii) Which prime number has been used maximum times?**

In the factors, 5 was used 3 times, 3 was used 2 times and all of the other prime numbers are used only once.

**Therefore, prime numbers 5 has been used maximum number of times.**

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