Discussion
What is the smallest positive integer which is not a factor of the product \(264 \times 90 \times 1680\)?
Answer: B
The smallest positive integer that is not a factor is 13.
Factorise each number and combine:
\[ \begin{aligned} 264 &= 2^{3} \times 3 \times 11 \\ 90 &= 2 \times 3^{2} \times 5 \\ 1680 &= 2^{4} \times 3 \times 5 \times 7 \\ \text{product} &= 2^{8} \times 3^{4} \times 5^{2} \times 7 \times 11 \end{aligned} \]
Every integer from 1 to 12 is built from these primes within these powers, so all divide the product (12 = 22 × 3). 13 is a prime that does not occur, so it is not a factor. 14 = 2 × 7 and 15 = 3 × 5 are factors.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development