Question

an army contingent of 616 members is to March behind an army band of 32 member 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 merge

Answer 1

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Answer 2

sol: Total no of members of army =616 and 32. since they March in same no. of columns. Maximum number of columns in which they March =H.C.F(616 and 32). Since 616 > 32. (1) Applying Euclid's division lemma on 616 and 31 we get. divident = divisor ✖ quotient + reminder .616 = 32 ✖ 19 + 18. reminder is not equal to 0. (2) Again applying Euclid's division lemma on 32 and 8 we get.Divident = divisor ✖ quotient + reminder. 32 = 8 ✖ 4 + 0. Reminder = 0. when reminder = 0 then divisor = 8. H.C.F. of 616 and 32 is 8. Hence maximum number of columns in which they March = 8.