What is the set A = {x ∈ ℕ : x is a factor of every natural number}?
Answer and explanation
Correct answer: {1}
The number 1 divides every natural number, so 1 satisfies the condition. No natural number greater than 1 divides every natural number: for example, if n > 1, then n does not divide n − 1. Also, 0 is not a factor because division by zero is undefined. Therefore the only element of A is 1, so A = {1}.
Frequently asked questions
What is the correct answer to this question?
{1}
Why is this the correct answer?
The number 1 divides every natural number, so 1 satisfies the condition. No natural number greater than 1 divides every natural number: for example, if n > 1, then n does not divide n − 1. Also, 0 is not a factor because division by zero is undefined. Therefore the only element of A is 1, so A = {1}.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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