Question

A group of 616 students is to march behind an army band of 32 members in a parade. The two groups must march in the same number of columns. What can be the maximum number of columns in which they march?

Answer 1

Hint: Here the given question is to solve for the number of columns in which the group must be divided so as to make the same number of columns for the students and the army band collectively. To solve such questions we need to understand the concept of highest common factor.
Formulae Used: Highest common factor of two or more numbers can be obtained by factorization of every number and then the highest common factor between all the numbers would give the HCF.

Complete step-by-step solution:
Here to solve the given question we will use the concept of the highest common factor, because by calculating the highest common factor we will obtained the maximum number of columns so that the students and the army band member can collectively make groups in equal number of members for the given columns, here on solving we get:
Highest common factor of 616 and 32 is given by:
\[
   \Rightarrow 616 = 2 \times 2 \times 2 \times 7 \times 11 \\
   \Rightarrow 32 = 2 \times 2 \times 2 \times 2 \times 2 \\
   \Rightarrow HCF = 2 \times 2 \times 2 = 8 \]
Here the HCF comes out to be eight, hence eight is the required number of columns.

Note: Highest common factor can be calculated by obtaining the highest common factor between two or more numbers collectively. Here we need to first make factorization in order to get the roots and then select the highest possible factor.