Question

two positive number have their HCF is 12 and their product at 6336 the number of pairs possible for the numbers is​

Answer 1

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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Answer 2

Answer:

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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