The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of numbers satisfying the above… · ABC26GN0486

Let the required numbers be $33 a$ and $33 b$. Then, $33 a+33 b=528 \Rightarrow a+b=16$. Now, co-primes with sum 16 are (1, 15), (3, 13), $(5,11)$ and (7, 9). $\therefore \quad$ Required numbers are ( $33 \times 1,33 \times 15$ ), ( $33 \times 3,33$ × 13), $(33 \times 5,33 \times 11),(33 \times 7,33 \times 9)$. The number of such pairs is 4.