Question

Find the greatest number that will divide $3026$ and $5053$ leaving remainders $11$ and $13$ respectively?

• A. $15$
• B. $30$
• C. $45$
• D. $60$

Answer 1

The correct option is C $45$

Required number=$HCFof(3026-11,5053-11)=HCFof(3015,5040)$

$3015=3\times 3\times 5\times 67=3^2\times 5\times 67$

$5040=2\times 2\times 2\times 2\times 3\times 3\times 5\times 7=2^4\times 3^2\times 5\times 7$

$\therefore$ HCF of $(3015,5040)=3^2\times 5=9\times 5=45$

Hence the greatest number is $45$.