The sum of two numbers is 528 and their H.C.F is 33. Find the number of pairs of such numbers satisfying the above condition?
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Solution
Let the required number is 33aand33b then 33a+33b=528 =>(a+b)=52833=16 no. of pairs with sum 16 are (1,15),(3,13),(5,11),(7,9) therefore there are 4 pairs which are (33×1,33×15) (33×3,33×13) (33×5,33×11) (33×7,33×9)