Q: A number is divisible by 6 if it is divisible by both:

The correct answer is 2 and 3. Explanation: Since $6 = 2 \times 3$ (where 2 and 3 are co-prime), a number must be divisible by both 2 and 3 to be divisible by 6.

Question 1

Which of the following is the smallest prime number?

Accepted Answer

The correct answer is 2. Explanation: A prime number is a natural number greater than 1 that has exactly two factors: 1 and the number itself. The smallest natural numbers are 1, 2, 3, 4... 1 is neither prime nor composite. 2 is the smallest prime number (and also the only even prime number).

Question 2

Which of the following pairs of numbers are co-prime?

Accepted Answer

The correct answer is 4 and 15. Explanation: Two numbers are co-prime if their Highest Common Factor (HCF) is 1. Factors of 4 = 1, 2, 4 Factors of 15 = 1, 3, 5, 15 Common factor = 1. Hence, HCF = 1. Thus, 4 and 15 are co-prime.

Question 3

What is the HCF of two consecutive natural numbers?

Accepted Answer

The correct answer is 1. Explanation: Two consecutive natural numbers (like 4 and 5, or 12 and 13) have no common factors other than 1. Hence, their HCF is always 1.

Question 4

A number is divisible by 6 if it is divisible by both:

Accepted Answer

The correct answer is 2 and 3. Explanation: Since $6 = 2 	imes 3$ (where 2 and 3 are co-prime), a number must be divisible by both 2 and 3 to be divisible by 6.

Question 5

Find the Highest Common Factor (HCF) of 12 and 18.

Accepted Answer

The correct answer is 6. Explanation: Prime factorisation of $12 = 2 	imes 2 	imes 3$ Prime factorisation of $18 = 2 	imes 3 	imes 3$ Common prime factors = $2 	imes 3 = 6$. Therefore, $	ext{HCF}(12, 18) = 6$.

Playing with Numbers