If \(A=\{x\in\mathbb{N}:x\mid36\}\) and \(B=\{x\in\mathbb{N}:x\mid48\}\), what is \(A\cap B\)?
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Answer and explanation
Correct answer: \(\{1,2,3,4,6,12\}\)
The positive divisors of 36 are \(\{1,2,3,4,6,9,12,18,36\}\), while those of 48 are \(\{1,2,3,4,6,8,12,16,24,48\}\). The common elements are therefore \(1,2,3,4,6,12\). Equivalently, common divisors are the divisors of \(\gcd(36,48)=12\), giving option A.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4,6,12\}\)
Why is this the correct answer?
The positive divisors of 36 are \(\{1,2,3,4,6,9,12,18,36\}\), while those of 48 are \(\{1,2,3,4,6,8,12,16,24,48\}\). The common elements are therefore \(1,2,3,4,6,12\). Equivalently, common divisors are the divisors of \(\gcd(36,48)=12\), giving option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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