Find the greatest number that divides $20, 30, 40$ leaving the remainder $2, 6, 4$ respectively.

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Solution

Step 1: Subtract the remainders from the given numbers:
$\begin{array}{rcl} 20 - 2 & = & 18 \\ 30 - 6 & = & 24 \\ 40 - 4 & = & 36 \end{array}$
Step 2: Now calculate the HCF:
$\begin{array}{rcl} 18 & = & 3 x 3 x 2 \\ 24 & = & 2 x 2 x 2 x 3 \\ 36 & = & 2 x 2 x 3 x 3 \end{array}$
Now HCF $(18, 24, 36) = 3 x 2 = 6$
Hence, $6$ is the greatest number.

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