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?

Hint – Here we will proceed from the integer which is larger and then apply Euclid’s division lemma to both the integers. Then we will repeat the algorithm up to the time we get remainder as zero. Hence we will get the desired result.

According to Euclid’s division lemma, if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition $a = b \times q + r$ where $0 < = r < = b$.
$\Rightarrow 616 > 32$
$\Rightarrow 616 = 32 \times 19 + 8$
$\Rightarrow 32 = 8 \times 4 + 0$