Math exercise challenging students to find factors, multiples, and prime numbers within a provided set of integers.

Explanation:
Let’s go through each part carefully.

Question 9: Numbers given: 6, 10, 11, 16, 24, 30, 40

(a) *Write down a multiple of 20*
A multiple of 20 is any number you get by multiplying 20 by a whole number:
20 × 1 = 20
20 × 2 = 40
20 × 3 = 60, etc.
From the list, only 40 is a multiple of 20 (since 40 ÷ 20 = 2, a whole number). ✔

(b) *Write down a factor of 12*
A factor of 12 is a number that divides 12 evenly (no remainder).
Factors of 12: 1, 2, 3, 4, 6, 12
From the list: 6 is there, and 12 ÷ 6 = 2 → yes, it’s a factor.
Also check others:
10? 12 ÷ 10 = 1.2 → no
11? no
16? too big
24? too big
30? no
40? no
So only 6 works from the list. ✔

(c) *Write down a prime number*
A prime number has exactly two positive factors: 1 and itself.
Check each number:
- 6 → factors: 1, 2, 3, 6 → not prime
- 10 → 1, 2, 5, 10 → not prime
- 11 → factors: 1 and 11 only → prime ✔
- 16 → divisible by 2, 4, 8 → not prime
- 24 → not prime
- 30 → not prime
- 40 → not prime
So only 11 is prime in the list.

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Question 10: Numbers: 15, 16, 17, 18, 20, 22, 24, 29

(a) *Write down a prime number*
Check each:
- 15 → 1, 3, 5, 15 → not prime
- 16 → even > 2 → not prime
- 17 → only divisible by 1 and 17 → prime ✔
- 18 → even → not prime
- 20 → even → not prime
- 22 → even → not prime
- 24 → even → not prime
- 29 → let’s test: not divisible by 2, 3 (2+9=11 not divisible by 3), 5 (doesn’t end in 0/5), 7? 7×4=28, 7×5=35 → no. So 29 is also prime.
But the question says “Write down a prime number” — just one is needed. Either 17 or 29 is fine. Since 17 comes first, we can pick 17.

(b) *Write down a factor of 30*
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
From the list:
- 15 → 30 ÷ 15 = 2 → yes ✔
- Others: 16? no, 17? no, 18? 30 ÷ 18 = 1.666… no, 20? 30 ÷ 20 = 1.5 no, 22? no, 24? no, 29? no
So only 15 works.

(c) *Write down a multiple of 3, which is even*
Multiple of 3: divisible by 3
Even: divisible by 2
So we need a number divisible by both 2 and 3 → divisible by 6.
Check numbers:
- 15 → divisible by 3, but odd → no
- 16 → even, but 1+6=7 not divisible by 3 → 16 ÷ 3 = 5.33 → no
- 17 → no
- 18 → 18 ÷ 3 = 6, and 18 is even → yes ✔
- 20 → 2+0=2 not divisible by 3 → no
- 22 → 2+2=4 → no
- 24 → 24 ÷ 3 = 8, and 24 is even → also yes ✔
- 29 → no
So both 18 and 24 work. The question asks for *a* (one) such number. We can choose 18 (first one).

Now double-check all answers against the lists to ensure they’re actually in the given numbers.

✔ Q9(a): 40 — in list
✔ Q9(b): 6 — in list
✔ Q9(c): 11 — in list
✔ Q10(a): 17 — in list
✔ Q10(b): 15 — in list
✔ Q10(c): 18 — in list

All correct.

Final Answer:
9. (a) 40
 (b) 6
 (c) 11
10. (a) 17
 (b) 15
 (c) 18