Question

Question 5
The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is

A) 13
B) 65
C) 875
D) 1750

Answer 1

Given that the number leaves a remainder 5 when it divides 60, and a remainder 8 when it divides 125.
Thus, this number must divide 70-5 = 65 and 125 - 8 = 117.

Now, the required number = HCF of 65, 117 [for the largest number]
For this, $117=65\times 1+52[\therefore dividend=divisor\times quotient+remainder]$
$\Rightarrow 65=52\times 1+13$
$\Rightarrow 52=13\times 4+0$
$\Rightarrow HCF=13$
Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

The answer is A.