Question : P = 25 × 38 and Q = 23 × 3K. If the highest common factor of P and Q is 23 × 33, then what is the value of K?
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 5
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Correct Answer: 3
Solution : Given: P = 2 5 × 3 8 and Q = 2 3 × 3 K The HCF of P and Q = 2 3 × 3 3 ⇒ HCF(2 5 × 3 8 , 2 3 × 3 K ) = 2 3 × 3 3 By comparison, the value of K = 3. Hence, the correct answer is 3.
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