Question

3. 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

Answer:

• Maximum number of columns = 8

Step-by-step explanation:

Given:

• An army contingent of 616 members is to march behind an army band of 32 members in
• a parade.
• Two groups march together in the same columns.

To find:

• Maximum number of columns in which they can march.

Solution:

Maximum number of columns can be found by finding the HCF of 32 and 616. Let us find HCF(32,616) by Euclid's division algorithm.

On applying Euclid's Division Algorithm, we get:

⟹ 616 = 32×19+8

⟹ 32 = 8×4+0

Since, the remainder is 0, the divisor is considered as the HCF of 32 and 616.

⟹ HCF(616,32) = 8

Hence, the maximum number of columns in which the groups can march are 8.

Note:

HCF can also be calculated by prime factorization method. It is the product of common prime factors of smallest power.

Answer 2

$\huge \fbox \red{Solution:}$

Given:

An army contingent of 616 members is to march behind an army band of 32 members in a parade. Also, the two groups are to march in the same number of columns.

Thus, we need to find the maximum number of columns in which they can march.

This is done by simply finding the HCF of the given two numbers.

Therefore, the maximum number of columns = H.C.F of 616 and 32.

$\fbox \blue{By applying Euclid’s division lemma}$

616 = 32 x 19 + 8

32 = 8 x 4 + 0.

So, H.C.F. = 8

$\fbox \blue{∴ The maximum number of columns in which they can march is 8.}$

$\bold\orange{Thanks}$