3. a) List the prime numbers up to 40 . b) Is 57 a prime number? Explain. 4. Find the HCF and LCM for these sets of numbers using prime factors \( \begin{array}{ll}\text { a) } 40 \text { and } 56 & \text { b) } 60 \text { and } 150\end{array} \) 5. Aysha has 136 buttons and eight containers. Can she divide the but equally between the containers?

The prime numbers up to 40 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37. Now, for 57, it’s not a prime number because it can be divided evenly by 3 (57 = 3 × 19), so it has factors beyond just 1 and itself. To find the HCF and LCM using prime factors, first, we break down the numbers: a) For 40 (2^3 × 5^1) and 56 (2^3 × 7^1), the HCF is 8 (2^3) and the LCM is 280 (2^3 × 5^1 × 7^1). b) For 60 (2^2 × 3^1 × 5^1) and 150 (2^1 × 3^1 × 5^2), the HCF is 30 (2^1 × 3^1 × 5^1) and the LCM is 300 (2^2 × 3^1 × 5^2). Aysha has 136 buttons and 8 containers, and yes, she can divide them equally! When you divide 136 by 8, you get 17, meaning each container can hold 17 buttons without any leftovers. Perfectly even distribution!