Question
data-sheets-value="{"1":2,"2":"The sum of two numbers is 104 and their HCF is 13. Total number of such pairs of numbers is "}" data-sheets-userformat="{"2":4993,"3":{"1":0},"10":2,"11":4,"12":0,"15":"arial,sans,sans-serif"}">The sum of two numbers is 104 and their HCF is 13. Total number of such pairs of numbers is?
Solution
As HCF is 13 so let numbers be 13x & 13y. It means x & y must be co-prime. Now 13x+ 13y = 104, So x + y = 8. Now pairs of (x , y) can be (1,7) , (2,6) , (3, 5) & (4,4) but (2,6) and (4,4) are not co-prime hence number of pairs are 2.
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