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Question

Two positive numbers have their HCF as 12 and their product as 6336. Choose the correct option for the number of pairs possible for the given numbers.

A
2
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B
3
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C
4
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D
5
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Solution

The correct option is A 2
Let the numbers be 12x and 12y, where x and y are co-primes.
Product of the numbers = 144xy
144xy=6336
xy=44
44 can be written as the product of two factors in three ways, i.e., 1×44,2×22,4×11
As x and y are relatively prime, (x,y) can be (1,44) or (4,11) but not (2,22).
Hence two possible pairs exist.

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