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?

Given

An army contingent of 616 members is to march behind an army band of 32 members in a parade.

Find out

The maximum number of columns in which they can march

Solution

The maximum number of columns in which they can march = HCF (32, 616)

So can use Euclid’s algorithm to find the HCF

Since 616 > 32, applying Euclid’s Division Algorithm we have

616 = 32 x 19 + 8

Since remainder ≠ 0

we again apply Euclid’s Division Algorithm

Since 32 > 8

32 = 8 × 4 + 0

Since remainder = 0 we conclude, 8 is the HCF of 616 and 32.

The maximum number of columns in which they can march is 8.

Answer

The maximum number of columns in which they can march is 8.

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