Discussion
The greatest number which can divide the numbers 282, 696 and 1616, leaving the same remainder 6 in each case, is :
Answer: D
The greatest such number is 46.
If each number leaves remainder 6, then subtracting 6 from each gives numbers the divisor divides exactly. The greatest such divisor is their HCF.
\[ \begin{aligned} 282 - 6 &= 276 \\ 696 - 6 &= 690 \\ 1616 - 6 &= 1610 \end{aligned} \]
\[ \begin{aligned} \text{HCF}(276, 690) &= 138 \\ \text{HCF}(138, 1610) &= 46 \end{aligned} \]
Check: \(276 = 46 \times 6\), \(690 = 46 \times 15\) and \(1610 = 46 \times 35\). 23 also divides all three but is not the greatest; 24 and 48 do not divide 690, so they leave different remainders.
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