Question

$N=\mathrm{9876543298765432.........82}$ digits. Find the remainder when N is divided by 34.

• A. 1
• B. 15
• C. 30

Answer 1

The correct option is C 30

Use Divisibility Rules -

$34=17\times 2$

So we should use the divisibility test of 17 (Compartmentalization method - taking 8 digits at a time, Sum of digits at odd places taken 8 at a time - Sum of digits at even places taken 8 at a time)

Combine 8 digits together, $\mathrm{9876......80}$ digits$\times 100+98.$

There will be an equal number of groups (of 8 digits taken at a time) at odd places and even.

Places in $\mathrm{9876......80}$ digits$\times 100.$

So, sum of groups at odd places - Sum of groups at even places = 0

Therefore first part is divisible by 17. It is also divisible by 2, as 100 is divisible by 2. Hence, we only need to find the remainder when 98 is divided by 34.

Remainder = 30