Question:
Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)
Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)
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Highest prime factor of a prime number is the number itself. For composite numbers, factorize completely and pick the largest prime.
Updated On: Jun 4, 2026
- \( \{5, 7, 13\} \)
- \( \{5, 7, 11, 13\} \)
- \( \{3, 5, 7, 11, 13\} \)
- \( \{3, 7, 11, 13\} \)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
We need the range of \(f\), i.e., the set of highest prime factors of each element in \(A\).
Step 2: Key Formula or Approach:
Factorize each number and identify the largest prime factor.
Step 3: Detailed Explanation:
\(10 = 2 \times 5\) → highest prime factor = 5
\(11\) → prime, highest prime factor = 11
\(12 = 2^2 \times 3\) → highest prime factor = 3
\(14 = 2 \times 7\) → highest prime factor = 7
\(26 = 2 \times 13\) → highest prime factor = 13
Set of these highest prime factors = \(\{5, 11, 3, 7, 13\} = \{3, 5, 7, 11, 13\}\).
Step 4: Final Answer:
Option (C) is correct.
We need the range of \(f\), i.e., the set of highest prime factors of each element in \(A\).
Step 2: Key Formula or Approach:
Factorize each number and identify the largest prime factor.
Step 3: Detailed Explanation:
\(10 = 2 \times 5\) → highest prime factor = 5
\(11\) → prime, highest prime factor = 11
\(12 = 2^2 \times 3\) → highest prime factor = 3
\(14 = 2 \times 7\) → highest prime factor = 7
\(26 = 2 \times 13\) → highest prime factor = 13
Set of these highest prime factors = \(\{5, 11, 3, 7, 13\} = \{3, 5, 7, 11, 13\}\).
Step 4: Final Answer:
Option (C) is correct.
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