Question

The sum of the two numbers is 588 and their HCF is 49. How many such pairs of numbers can be
formed?

Answer 1

Answer:

49 = 7^2 is the greatest common factor, thus both numbers must contain 7^2. So, one pair would be: 49 and 539 (from 588-49).

Answer 2

Let the numbers be 49a and 49b, where a and b are co-primes.

Then,

49a + 49b = 588

49 (a + b) = 588

a + b = 12

Therefore,

(a=1,b=11), (a=2,b=10), (a=3,b=9), (a=4,b=8), (a=5,b=7), (a=6,b=6)

Therefore, the possible number of pairs = 6

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