Teaching Mathematics through activities is a powerful . . .

Question : 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 multiply 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 the students? [1 Mark]

(ii) 

(a) How many students are in the class? [2 Marks]
OR

(b) What is the highest prime number used by the students? [2 Marks]

(iii) Which prime number has been used maximum times? [1 Mark]

CBSE Outside Delhi [2024] (30/3/1)

Solution : 

Here the final number obtained by the last students is 173250. 

Since all the students have multiplied prime numbers only so we can get all the multiplied prime numbers back by prime factorisation of final number obtained which is 173250.

173250=2×3×3×5×5×5×7×11

173250=2×3²×5³×7×11

(i) What is the least prime number used by the students?

Ans : Least Prime number is 2 but it is given by the teacher not the student. So the least prime number used by the student is 3 and not 2. 

(ii)

(a) How many students are in the class?
Ans : Number of students in the class will be equal to prime factors of 173250 except the first number 2.

173250=2×3×3×5×5×5×7×11

So, there are 7 students in the class. 

OR

(b) What is the highest prime number used by the students?

Ans : 

173250=2×3×3×5×5×5×7×11

Clearly, highest prime number used by the student is 11.

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

Ans : 

173250=2×3×3×5×5×5×7×11

From the above prime factorisation it is clear that the prime factor 5 has been used maximum times (5 times).