Question

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?

Answer 1

Let the required number is $33aand33b$
then $33a+33b=528$
$=>(a+b)=\frac{528}{33}=16$
no. of pairs with sum 16 are $(1,15),(3,13),(5,11),(7,9)$
therefore there are $4$ pairs which are
$(33\times 1,33\times 15)$
$(33\times 3,33\times 13)$
$(33\times 5,33\times 11)$
$(33\times 7,33\times 9)$