Mr Japheth wants to put all 26 girls and 78 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 Japheth can form with these conditions?
- How many students are in each group?
(a)
Factors of 26 = 1, 2, 13, 26
Factors of 78 = 1, 2, 3, 6, 13, 26, 39, 78
Greatest number of groups Mr Japheth can form
= Highest common factor of 26 and 78
= 26
(b)
Number of girls in each group = 26 ÷ 26 = 1
Number of boys in each group = 78 ÷ 26 = 3
Number of students in each group
= 1 + 3
= 4
Answer(s): (a) 26; (b) 4