Question

The greatest number which can divide $1854,1866$ and $2066$ leaving the same remainder $2$ in each case is:

• A. $4$
• B. $6$
• C. $12$
• D. none of the above

Answer 1

The correct option is A $4$

The largest number divides all these numbers leaving remainder 2 in each case.

Thus, we conclude that the required number will be the HCF of the numbers so obtained after subtracting 2 from each of the given numbers.
$1854-2=1852=4\times 463$
$1866-2=1864=4\times 466$
$2066-2=2064=4\times 516$
HCF is $4$.