Question

What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ?

• A. 16

Answer 1

The correct option is A 16

Since the remainder is 5 in both the cases, we have to subtract 5 from each number.
$245-5=240\text{and}1029-5=1024$

Now, we have to find the H.C.F of 240 and 1024.

By Euclid's division lemma,
$a=bq+r,0\le r<b$

$\text{Here, a = 1024 and b = 240}1024=240\times 4+64240=64\times 3+4864=48\times 1+1648=16\times 3+0$

Therefore, H.C.F is 16.
So, the largest number that divides 245 and 1029 leaving remainder 5 in each case is 16.