Question

There are 44 boys and 32 girls in a class. These students are arranged in rows for a prayer in such
a way that each row consists of only either boys or girls, and every row contains an equal number
of students. Find the minimum number of rows in which all the students can be
arranged.​

Answer 1

Answer:

For number of rows to be least the number of students in each row should be the highest, so we need to find the hcf ( we find hcf when we have to split things into smaller sections or arrange sth. into rows or columns)

H.C.F of 44 and 32 :

prime factorisation of 44: 2^2×11

prime factorisation of 32: 2^5

H.C.F is the product of common prime factors with lesser index(power)

so here 2^2 has the lesser power and is common to both 44 and 32

H C.F = 4

minimum no. of rows = 44/4 + 32/4 = 11+8 = 19(Ans.)