Case Based Questions: Prime Time | Mathematics for Class 6 PDF Download

Q1: Read the source and answer the question that follows

In a school library, there are 780 books of English and 364 books of Science. Ms. Yakang, the librarian of the school wants to store these books in shelves such that each shelf should have the same number of books of each subject

Q1. What is the prime factorisation of 780 and 364.?

Ans. Factors of 780= 2 × 2 × 3 × 5 × 13

And 364 = 2 × 2 × 7 × 13

Q2. What should be the minimum number of books in each shelf?

Ans. By given value in school library
Factorisation of 780 = 2 × 2 × 3 × 5 × 13
And 364 = 2 × 2 × 7 × 13
The common factors are 2 × 2 × 13 = 52
So, the minimum number of books in each shelf is 52.

Q3. How many factors are common in 780 and 364.?

Ans. Common factors are 2 and 13
So, there are two common factors.

Q2: Read the source and answer the question that follows

Ravi and Tanya were having a discussion in class about prime numbers. Ravi was curious about what made prime numbers so special, and Tanya explained that a prime number is a number greater than 1 that can only be divided evenly by 1 and itself. For example, 7 is a prime number because the only numbers that divide 7 exactly are 1 and 7. Tanya also pointed out that numbers like 12, 15, and 30 are not prime numbers because they have more divisors other than 1 and themselves.Q1. What is a prime number?
(a) A number divisible by 1 and itself
(b) A number divisible by any number
(c) A number greater than 10
(d) A number that is even

Ans: (a) A number divisible by 1 and itself.
Explanation: A prime number is a number greater than 1 that can only be divided evenly by 1 and itself.

Q2. Which of the following is a prime number?
(a) 12
(b) 15
(c) 7
(d) 30

Ans: (c) 7
Explanation: 7 is a prime number because it only has two divisors, 1 and 7.

Q3. Why is 12 not a prime number?
Ans: 12 is not a prime number because it has divisors other than 1 and itself, such as 2, 3, 4, and 6.

Q3: Read the source and answer the question that follows

Amit and Kavita were discussing the concept of parity. Amit asked, "What happens if we add two odd numbers?" Kavita explained that the sum of two odd numbers is always even. They tried adding 3 and 5, and the sum was 8, which is even. Kavita also mentioned that the sum of three odd numbers will always be odd.

Q1. What happens when you add two odd numbers?
(a) The result is always odd
(b) The result is always even
(c) The result is always prime
(d) The result is always divisible by 3

Ans: (b) The result is always even.
Explanation: The sum of two odd numbers is always even.

Q2. What is the sum of three odd numbers?
(a) Always even
(b) Always odd
(c) Always divisible by 2
(d) Always prime

Ans: (b) Always odd.
Explanation: The sum of three odd numbers is always odd.