The largest number which divides

(a) Since, 5 and 8 are the remainders of 70 and 125, respectively. Thus, after subtracting these remainders from the numbers, we have the numbers

65 = (70-5),

117 = (125 – 8), which is divisible by the required number.

Now, required number = HCF of 65,117                                     [for the largest number]

For this, $\quad 117=65 \times 1+52 \quad[\because$ dividend $=$ divisor $\times$ quotient $+$ remainder $]$

$\Rightarrow \quad 65=52 \times 1+13$

$\Rightarrow \quad 52=13 \times 4+0$

$\therefore \quad \quad \mathrm{HCF}=13$

Hence, 13 is the largest number which divides 70 and 125 , leaving remainders 5 and 8 .