Let $A = \{x \in N : x \text{ is a factor of } 24\}$ and $B = \{x \in N : x \text{ is a factor of } 36\}$. Find $A \cap B$ and identify its greatest element.

Let A = \x ∈ N : x is a factor of 24\ and B = \x ∈ N : x is a factor of 36\. Find A ∩ B and identify its great

Miscellaneous · Q27

A = \{x \in N : x \text{ is a factor of } 24\}

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Factors of 24: $\{1,2,3,4,6,8,12,24\}$ . Factors of 36: $\{1,2,3,4,6,9,12,18,36\}$ . The common factors (appearing in both lists) are $1,2,3,4,6,12$ — so $A \cap B = \{1,2,3,4,6,12\}$ . The greatest element of this intersection is 12, which is exactly $\gcd(24,36)$ (since $24=2^3\times3$ , $36=2^2\times3^2$ , and $\gcd=2^2\times3=12$ ) — the intersection of the factor sets of …

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Q.Let $A = \{x \in N : x \text{ is a factor of } 24\}$ and $B = \{x \in N : x \text{ is a factor of } 36\}$ . Find $A \cap B$ and identify its greatest element.

Concept understanding — Union and Intersection of Sets

Q.Let A={x∈N:x is a factor of 24}A = \{x \in N : x \text{ is a factor of } 24\}A={x∈N:x is a factor of 24} and B={x∈N:x is a factor of 36}B = \{x \in N : x \text{ is a factor of } 36\}B={x∈N:x is a factor of 36}. Find A∩BA \cap BA∩B and identify its greatest element.

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Q.Let $A = \{x \in N : x \text{ is a factor of } 24\}$ and $B = \{x \in N : x \text{ is a factor of } 36\}$ . Find $A \cap B$ and identify its greatest element.

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