Let S be the set of all ordered pairs (x,y) of positive integers, with

1.	Let S be the set of all ordered pairs (x,y) of positive integers, with HCF (x,y) = 16 and LCM (x,y) = 48000. The number of elements in S is (A) 4 (B) 8 (C) 16 (D) 32
Answer» Correct Option :- (B) 8 Explanation :- 48000 = 16 × 3000 = 16 × [3¹× 2³ × 5³ ] As H.C.F. is 16 So 2³ can be selected in 1 way & 3¹ × 5³can be seleted in (1+ 1) (3 +1) = 8 ways No of ordred pairs = 8

Let S be the set of all ordered pairs (x,y) of positive integers, with HCF (x,y) = 16 and LCM (x,y) = 48000. The number of elements in S is (A) 4 (B) 8 (C) 16 (D) 32

Answer»

Correct Option :- (B) 8

Explanation :-

48000 = 16 × 3000 = 16 × [3¹× 2³ × 5³ ]

As H.C.F. is 16 So 2³ can be selected in 1 way & 3¹ × 5³can be seleted in (1+ 1) (3 +1) = 8 ways

No of ordred pairs = 8

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Let S be the set of all ordered pairs (x,y) of positive integers, with HCF (x,y) = 16 and LCM (x,y) = 48000. The number of elements in S is (A) 4 (B) 8 (C) 16 (D) 32

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