Children's home

Nicholas gave the children's home 54 oranges, 81 chocolate figurines, and 135 apples as gifts. Every child received the same gift, and nothing was left.

a) How many packages could be prepared?
b) what did the children find in the package?

Correct answer:

n =  27
p =  2
c =  3
j =  5

Step-by-step explanation:

$$\begin{gathered} 54=2\cdot 3^3 \\ 81=3^4 \\ 135=3^3\cdot 5 \\ \text{GCD}(54,81,135)=3^3=27 \\ n=GCD(54,81,135)=27 \end{gathered}$$

$p=54/n=54/27=2$

$c=81/n=81/27=3$

$j=135/n=135/27=5$

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