Question:
Find the maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils.
Solution:
Total number of pens = 1001
Total number of pencils = 910
∴ Maximum number of students who get the same number of pens and pencils = HCF (1001, 910)
Prime factorisation:
$1001=11 \times 91$
$910=10 \times 91$
$\therefore \mathrm{HCF}=91$
Hence, 91 students receive same number of pens and pencils.