Discussion
The number of positive divisors of 8000 is :
Answer: C
8000 has 28 positive divisors.
Write 8000 as a product of prime powers, then add 1 to each exponent and multiply:
\[ \begin{aligned} 8000 &= 8 \times 1000 = 2^{3} \times 2^{3} \times 5^{3} \\ &= 2^{6} \times 5^{3} \\ d(8000) &= (6+1)(3+1) = 28 \end{aligned} \]
Each divisor is \(2^{a}5^{b}\) with a from 0 to 6 (7 choices) and b from 0 to 3 (4 choices). 25, 26 and 18 do not match this count; 18, for instance, would need exponents such as 5 and 2, which do not give 8000.
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