If K = {x ∈ ℕ : x divides 12 exactly}, which is the roster form of K?
Answer and explanation
Correct answer: {1, 2, 3, 4, 6, 12}
A positive natural number divides 12 exactly when the remainder is zero. Checking the positive factors gives 1, 2, 3, 4, 6, and 12: 12 ÷ each of these is an integer. The number 1 and 12 itself must both be included. Zero cannot be a divisor, so option D is invalid, and option A lists all factors without omission.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4, 6, 12}
Why is this the correct answer?
A positive natural number divides 12 exactly when the remainder is zero. Checking the positive factors gives 1, 2, 3, 4, 6, and 12: 12 ÷ each of these is an integer. The number 1 and 12 itself must both be included. Zero cannot be a divisor, so option D is invalid, and option A lists all factors without omission.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
