Question

an army contingent of 616 members is to March behind an army band of 32 members in parade the two group are to March in same number of columns in which they can march​

Answer 1

Total number of members = 616.

The total number of members are to march behind an army band of 32 members is HCF of 616 and 32.

i.e., HCF of 616 and 32 is equal to the maximum number of columns such that the two groups can march in the same number of columns.

therefore, applying Euclid's Division Lemma to 616 and 32,

we get

616 = 32 ×19 +8

32 = 8 × 4 + 0

hence HCF of 616 and 32 is 8.

Hence, the required number of maximum columns = 8.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

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.