Question

A sweet seller has 420 kaju barfis and 140 badam barfis . She wants to stack them un such a way that each stack has the same number , and they take up the least space of the tray . What is the number of barfis that can be placed in each stack .

Answer 1

To stack equal number of barfis in each pile, we will have to calculate such a number which divides 420 and 140 each so that no extra barfi remain there. such a number is always the H.C.F.of the given numbers. So,we calculate the hcf of 420 and 140. 
By prime factorisation -- 
420= 2*2*3*5*7
140 = 2*2*5*7
taking the common factors, we get - 2*2*5*7 which is 140.
so, she should stack 140 barfis in each pile.

Answer 2

$\large \bigstar{\underline{\green{\mathfrak Answer:}}}$

The sweetseller can make stacks of 10 for both kinds of burfis to cover the least area of the stack

$\bold{\underline {Given:}}$

A sweet seller has 420 kaju barfies and 130 badam barfies she wants to stack them in such a way that each stack has the same number.

$\bold{\underline {To\:Find :}}$

The least area of the tray what is the number that can be placed in each stack for this purpose =?

$\large \bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Area of the tray will be least if the sweetseller stacks the maximum number of burfis in each stack.

Since each stack has the same number of burfis, therefore, the number of stack will be least if the number of burfis in each stack is equal to HCF of 420 and 130.

To find HCF of 420 and 130, we apply the Euclid's division lemma to 420 and 130.

We have

420 = 130 x 3 + 30

130 = 30 x 4 + 10

30 = 10 x 3 + 0

So, HCF of 420 and 130 is 10.

Therefore, the sweetseller can make stacks of 10 for both kinds of burfis to cover the least area of the stack