Question

There are 462 girls and 728 boys in a school. I
were to be arranged in groups pairing an equal number of
boys and girls, Find the maximum number of studends
Possible in each group.​

Answer 1

There are 462 girls and 728 boys in a school.

So, we have given that

→ Number of girls = 462

→ Number of boys = 728

We have to find the maximum number of students that are possible in each group.

To find the maximum number of students in each group we have to find the HCF.

Let's start with finding LCM of their and then HCF.

LCM of 462 :

$\begin{array}{l|r}2 & 462 \\ \cline{2-2} 3 & 231 \\ \cline{2-2} 7 & 77 \\ \cline{2-2} 11 & 11 \\ \cline{2-2} & 1 \end{array}$

=> 2 × 3 × 7 × 11

LCM of 728 :

$\begin{array}{l|r}2 & 728 \\ \cline{2-2} 2 & 364 \\ \cline{2-2} 2 & 182 \\ \cline{2-2} 7 & 91 \\ \cline{2-2} 13 & 13 \\ \cline{2-2} & 1 \end{array}$

=> 2 × 2 × 2 × 7 × 13

Both 2 and 7 is common in 462 and 728.

Common factor = 2 and 7

So,

HCF of 462 and 728 is 2 × 7

=> 14

•°• Maximum 14 students are possible in each group.

Answer 2

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