Solved Questions on Prime Factorisation
1. What is the prime factorisation of 441?
a) 3 x 3 x 7 x 7
b) 2 x 2 x 3 x 7 x 11
c) 2 x 2 x 2 x 3 x 3 x 7
d) 2 x 3 x 5 x 7
Answer: a) 3 x 3 x 7 x 7
Explanation: To find the prime factorisation of 441, we can start by dividing by 3 to get 147. 147 can be divided by 3 again to get 49, which is 7 x 7.
Therefore, the prime factorisation of 441 is 3 x 3 x 7 x 7.
2. Find the prime factorisation of the 393.
a) 2 x 2 x 7 x 8
b) 3 x 131
c) 3 x 4 x 8
d) 2 x 8 x 7 x 11
Answer: b) 3 x 131
Explanation: The prime factorisation of 393 is 3 x 131.
3. What is the smallest prime factor of 999?
a) 2
b) 3
c) 5
d) 7
Answer: b) 3
Explanation: To find the smallest prime factor of 999, we can start by dividing it by 2, which does not give an integer result.
Next, we can try 3, which divides 999 evenly, giving 333.
Therefore, the smallest prime factor of 999 is 3.
4. What is the prime factorisation of 2400?
a) 22 x 3 x 52
b) 22 x 3 x 5
c) 24 x 54
d) 25 × 31 × 52
Answer: d) 25 × 31 × 52
Explanation: The prime factorisation of 2,400 is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5.
5. Find the HCF and LCM of 646 and 782?
a) 32, 13428
b) 34, 14858
c) 38, 14938
d) 42, 15346
Answer: b) 34, 14858
Explanation: To find the HCF and LCM of 646 and 782, we can use the prime factorisation method:
Prime factorisation of 646: 2 × 17 × 19
Prime factorisation of 782: 2 × 17 × 23
To find the HCF, we need to identify the common factors of the two numbers. Therefore, the HCF of 646 and 782 is 2 × 17 = 34.
To find the LCM, we need to identify the highest power of each prime factor that appears in either number. The prime factors of the two numbers are 2, 17, 19, and 23. Therefore, the LCM of 646 and 782 is 2 × 17 × 19 × 23 = 14858.
Hence, the HCF of 646 and 782 is 34 and the LCM is 14858.
Practice Questions on Prime Factorisation
1. What is the prime factorisation of 360?
a) 2 x 2 x 2 x 3 x 3 x 5
b) 2 x 2 x 2 x 2 x 3 x 5
c) 3 x 3 x 3 x 5 x 5
d) 2 x 3 x 5 x 7
Answer: a) 2 x 2 x 2 x 3 x 3 x 5
2. What is the largest prime factor of 126?
a) 2
b) 3
c) 5
d) 7
Answer: d) 7
3. What is the smallest prime factor of 546?
a) 13
b) 7
c) 3
d) 2
Answer: d) 2
4. What is the prime factorisation of 2520?
a) 23 x 32 x 5 x 7
b) 22 x 3 x 5 x 72
c) 23 x 33 x 5 x 7
d) 2 x 32 x 5 x 72
Answer: a) 23 x 32 x 5 x 7
5. What is the prime factorisation of 1680?
a) 24 x 3 x 5 x 7
b) 24 x 3 x 5 x 72
c) 24 x 32 x 5 x 7
d) 24 x 3 x 52 x 7
Answer: b) 24 x 3 x 5 x 7
6. What is the prime factorisation of 750?
a) 2 x 2 x 2 x 3 x 3 x 5
b) 2 x 2 x 2 x 2 x 3 x 5
c) 2 x 3 x 5 x 5 x 5
d) 2 x 3 x 5 x 7
Answer: c) 2 x 3 x 5 x 5 x 5
8. What is the HCF of 28 and 42?
a) 2
b) 7
c) 14
d) 21
Answer: c) 14
9. What is the HCF of 1425 and 625?
a) 5
b) 15
c) 25
d) 35
Answer: c) 25
10. What is the prime factorisation of 756?
a) 2 x 2 x 3 x 3 x 3 x 7
b) 2 x 2 x 3 x 7 x 11
c) 3 x 3 x 3 x 7 x 7
d) 2 x 2 x 2 x 3 x 3 x 7
Answer: a) 2 x 2 x 3 x 3 x 3 x 7
