If A = {x : x is a prime divisor of both 24 and 36}, what is A?
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Answer and explanation
Correct answer: A = {2, 3}
The prime divisors of 24 are 2 and 3, because 24 = 2^3 × 3. The prime divisors of 36 are also 2 and 3, because 36 = 2^2 × 3^2. Therefore, the prime divisors common to both numbers are exactly 2 and 3, so A = {2, 3}. Number 1 is not prime, and 6 or 12 are composite, not prime.
Frequently asked questions
What is the correct answer to this question?
A = {2, 3}
Why is this the correct answer?
The prime divisors of 24 are 2 and 3, because 24 = 2^3 × 3. The prime divisors of 36 are also 2 and 3, because 36 = 2^2 × 3^2. Therefore, the prime divisors common to both numbers are exactly 2 and 3, so A = {2, 3}. Number 1 is not prime, and 6 or 12 are composite, not prime.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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