For T={x: x is a positive factor of 32}, what is n(T)?
Answer and explanation
Correct answer: 6
The governing concept is counting distinct positive factors using prime factorisation. Since 32=2⁵, every positive factor has the form 2^k where k=0,1,2,3,4,5. These give 1,2,4,8,16,32, six distinct factors. Therefore n(T)=6 and option C is correct. The factor 32 itself is included because a number divides itself; no additional positive factors exist.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The governing concept is counting distinct positive factors using prime factorisation. Since 32=2⁵, every positive factor has the form 2^k where k=0,1,2,3,4,5. These give 1,2,4,8,16,32, six distinct factors. Therefore n(T)=6 and option C is correct. The factor 32 itself is included because a number divides itself; no additional positive factors exist.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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