Prime Time
Short Answer Questions
1. What are multiples? Give an example.
Answer: Multiples are numbers obtained by multiplying a number with whole numbers.
Example: Multiples of 3 → 3, 6, 9, 12, …
2. What are common multiples?
Answer: Common multiples are numbers that are multiples of two or more numbers.
Example: Common multiples of 3 and 5 → 15, 30, 45 …
3. What are factors?
Answer: Factors are numbers that divide a given number exactly.
Example: Factors of 24 → 1, 2, 3, 4, 6, 8, 12, 24
4. What are common factors?
Answer: Common factors are factors that are common to two or more numbers.
Example: Common factors of 14 and 36 → 1, 2
5. Define prime numbers with an example.
Answer: Prime numbers have exactly two factors: 1 and the number itself.
Example: 7 (factors: 1 and 7)
6. Define composite numbers.
Answer: Composite numbers have more than two factors.
Example: 12 (factors: 1, 2, 3, 4, 6, 12)
7. Why is 1 neither prime nor composite?
Answer: Because it has only one factor (1).
8. What are co-prime numbers?
Answer: Two numbers that have no common factor except 1 are called co-prime numbers.
Example: 4 and 9
9. What is prime factorisation?
Answer: Writing a number as a product of prime numbers is called prime factorisation.
Example: 56 = 2 × 2 × 2 × 7
10. State the divisibility rule of 5.
Answer: A number is divisible by 5 if it ends with 0 or 5.
Long Answer Questions
1. Find the common factors of 20 and 28.
Solution:
Factors of 20 → 1, 2, 4, 5, 10, 20
Factors of 28 → 1, 2, 4, 7, 14, 28
Common factors → 1, 2, 4
2. Find the prime factorisation of 72.
Solution:
Step 1: 72 = 12 × 6
Step 2: 12 = 2 × 2 × 3
Step 3: 6 = 2 × 3
Step 4: Combine all factors
72 = 2 × 2 × 3 × 2 × 3
Step 5: Arrange
72 = 2 × 2 × 2 × 3 × 3
3. Check whether 56 and 63 are co-prime using prime factorisation.
Solution:
56 = 2 × 2 × 2 × 7
63 = 3 × 3 × 7
Common factor = 7
Therefore, 56 and 63 are NOT co-prime.
4. Find all jump sizes that will land on both 15 and 30.
Solution:
Step 1: Factors of 15 → 1, 3, 5, 15
Step 2: Factors of 30 → 1, 2, 3, 5, 6, 10, 15, 30
Step 3: Common factors → 1, 3, 5, 15
Step 4: (If 1 is not allowed) → 3, 5, 15
5. Check if 168 is divisible by 12 using prime factorisation.
Solution:
Step 1: Prime factorisation
168 = 2 × 2 × 2 × 3 × 7
12 = 2 × 2 × 3
Step 2: Compare factors
All factors of 12 are present in 168
Step 3: Conclusion
168 = 12 × 14
Therefore, 168 is divisible by 12.
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