Question

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

• A. 15
• B. 16
• C. 9
• D. 5

Answer 1

The correct option is B 16

We have to subtract 5 from each number:
$245-5=240$ & $1029-5=1024$
& then find the H.C.F 240 & 1024.

By Euclid division lemma, $a=bq+r$
$a=1024andb=2401024=240\times 4+64240=64\times 3+4864=48\times 1+1648=16\times 3+0$
Therefore, H.C.F is 16.