If \(A=\{x\in\mathbb{N}:x\mid 72\}\) and \(B=\{x\in\mathbb{N}:x\mid 90\}\), what is \(A\cap B\)?
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Answer and explanation
Correct answer: \(\{1,2,3,6,9,18\}\)
The intersection contains natural numbers that divide both 72 and 90. Therefore, its elements are exactly the positive divisors of \(\gcd(72,90)\). Since \(\gcd(72,90)=18\), the positive divisors are 1, 2, 3, 6, 9, and 18. Thus \(A\cap B=\{1,2,3,6,9,18\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,6,9,18\}\)
Why is this the correct answer?
The intersection contains natural numbers that divide both 72 and 90. Therefore, its elements are exactly the positive divisors of \(\gcd(72,90)\). Since \(\gcd(72,90)=18\), the positive divisors are 1, 2, 3, 6, 9, and 18. Thus \(A\cap B=\{1,2,3,6,9,18\}\), so option A is correct.
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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