Example 4 : A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number , and they take up the least area of the trya. What is the maximum number of barfis that can be placed in each stack for this purpose ?
Solution : this can be done by trial and error. But to do it systematically , we find HCF (420,130) . Then this number will give the maximum number of barfis in each stack and the number of stacks will then be the least. The area of the tray that is used up will be the least.
Now, let us use Euclid’s algorithm to find their HCF : We have :
420 = 130 x 3 + 30
130 =30x 4 +10
30 = 10 x 3 + 0
So, the HCF of 420 and 130 is 10.
Therefore, the sweetseller can make stacks of 10 for both kinds of barfis.
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