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?​

Answer 1

Given,

• Number of army contingent members = 616

• Number of army band members = 32

If the two groups have to march in the same column, we have to find out the highest common factor between the two groups.

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

By Using Euclid’s algorithm to find their HCF, we get,

Since, 616 > 32,

Therefore,

616 = 32 × 19 + 8

Since, 8 ≠ 0, therefore, taking 32 as new divisor, we have,

32 = 8 × 4 + 0

(Now we have got remainder as 0.)

Therefore,

HCF (616, 32) = 8.

Hence, the maximum number of columns in which they can march is 8.

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Answer 2

Answer:

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

Step 1: First find which integer is larger.

616>32

Step 2: Then apply the Euclid's division algorithm to 616 and 32 to obtain

616=32×19+8

Repeat the above step until you will get remainder as zero.

Step 3: Now consider the divisor 32 and the remainder 8, and apply the division lemma to get

32=8×4+0

Since the remainder is zero, we cannot proceed further.

Step 4: Hence the divisor at the last process is 8

So, the H.C.F. of 616 and 32 is 8.

Therefore, 8 is the maximum number of columns in which they can march.