Question

The largest number which divides $245$ and $1029$ leaving remainder $5$ is

• A. $15$
• B. $16$
• C. $5$
• D. $9$

Answer 1

Answer: (B)

$16$

Required number will be $HCF$ of $245-5=240$ and $1029-5=1024.$

So, by prime factorization,
$240=2\times 2\times 2\times 2\times 3\times 5$
$1024=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Hence,
$HCF(240,1024)=2\times 2\times 2\times 2$

$=16$

Therefore, $16$ is the largest number which divides $245$ and $1024$ leaving the remainder $5$ in each.