If H = {x : x is a natural number and x is a factor of 12}, what is H?
Answer and explanation
Correct answer: H = {1, 2, 3, 4, 6, 12}
The governing concept is membership by divisibility. A natural number is a factor of 12 when it divides 12 exactly, leaving remainder zero. The positive divisors are found from the factor pairs 1×12, 2×6, and 3×4, giving H = {1, 2, 3, 4, 6, 12}. Option B is mostly a list of even numbers, C contains multiples of 12, and D contains odd numbers, so only A is complete and correct.
Frequently asked questions
What is the correct answer to this question?
H = {1, 2, 3, 4, 6, 12}
Why is this the correct answer?
The governing concept is membership by divisibility. A natural number is a factor of 12 when it divides 12 exactly, leaving remainder zero. The positive divisors are found from the factor pairs 1×12, 2×6, and 3×4, giving H = {1, 2, 3, 4, 6, 12}. Option B is mostly a list of even numbers, C contains multiples of 12, and D contains odd numbers, so only A is complete and correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Common Questions. Topic: General chapter practice.
