Mr Ethan wants to put all 32 girls and 66 boys into groups for an activity. There are more boys than girls in each group. Each group must have the same number of girls. Each group must also have the same number of boys.
- What is the greatest number of groups Mr Ethan can form with these conditions?
- How many students are in each group?
(a)
Factors of 32 = 1, 2, 4, 8, 16, 32
Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Greatest number of groups Mr Ethan can form
= Highest common factor of 32 and 66
= 2
(b)
Number of girls in each group = 32 ÷ 2 = 16
Number of boys in each group = 66 ÷ 2 = 33
Number of students in each group
= 16 + 33
= 49
Answer(s): (a) 2; (b) 49