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

The answer is A.
Since 5 and 8 are the remainders respectively, after subtracting these remainders from the numbers,
We have the number 65 = (70 - 5), 117 = (125 - 8), which are divisible by the required numbers.
Now, 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.