How many elements are in the set {x ∈ ℕ : x is a factor of 36}?
Answer and explanation
Correct answer: 9
The governing concept is counting the positive natural-number divisors of a finite number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Each divides 36 exactly, and the list is complete; alternatively, 36 = 2² × 3², so the number of positive divisors is (2 + 1)(2 + 1) = 9. Hence option B is correct. The set is finite, so option D cannot be true.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The governing concept is counting the positive natural-number divisors of a finite number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Each divides 36 exactly, and the list is complete; alternatively, 36 = 2² × 3², so the number of positive divisors is (2 + 1)(2 + 1) = 9. Hence option B is correct. The set is finite, so option D cannot be true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
