Question

5931 students are sitting in an auditorium in such a manner that there are as many students in a row
as there are rows in the auditorium. How many students are left after the arrangement?

Answer 1

Step-by-step explanation:

Let there be

′

a

′

rows in the auditorium

Since the number of students in a row is same as the number of rows in the auditorium.

∴ Number of students in a row =a

⇒ Number of students in

′

a

′

rows =a×a=a

2

It is given that the total number of students in the auditorium =5929.

∴a

2

=5929

⇒a=

5929

7∣5929

7∣847

11∣121

∣11

⇒a=

(7×7)×(11×11)

[By prime factorisation]

⇒a=7×11 [Taking one factor in each pair]

⇒a=77

Hence, there are 77 rows in the auditorium.