# Ex.1.1 Q3 Real Numbers Solution - NCERT Maths Class 10

## Question

An army contingent of \(616\) members is to march behind an army band of \(32\) members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

## Text Solution

**What is known?**

We are told that there is an army contingent of \(616\) members and an army band of \(32\) members. The two groups are to march in the same number of columns

**What is unknown?**

The maximum number of columns in which they can march.

**Reasoning:**

Here, we have to pay attention to the point that the army band members and army contingent members have to march in the **same number of columns** and that the number of columns must be the **maximum** possible. The definition of HCF states – HCF of two positive integers *\(a\) *and *\(b\)* is the largest positive integer *\(d\)* that divides both *\(a\)* and *\(b\)*. In other words, HCF of two numbers is the highest number (maximum) that divides both the numbers. Thus, we have the find the HCF of the members in the army band and the army contingent.

**Steps:**

HCF (\(616, 32\)) will give the maximum number of columns in which they can march.

We use Euclid’s algorithm to find the H.C.F

\[\begin{align} 616&=(32\,\times \,19)\,+\,8 \\32&=(8\,\times \,4)+0\end{align}\]

The HCF (\(616, 32\)) is \(8.\) Therefore, they can march in \(8\) columns each.