Mr Warren wants to put all 21 boys and 78 girls into groups for an activity. There are more girls than boys in each group. Each group must have the same number of boys. Each group must also have the same number of girls.
- What is the greatest number of groups Mr Warren can form with these conditions?
- How many pupils are in each group?
(a)
Factors of 21 = 1, 3, 7, 21
Factors of 78 = 1, 2, 3, 6, 13, 26, 39, 78
Greatest number of groups Mr Warren can form
= Highest common factor of 21 and 78
= 3
(b)
Number of boys in each group = 21 ÷ 3 = 7
Number of girls in each group = 78 ÷ 3 = 26
Number of pupils in each group
= 7 + 26
= 33
Answer(s): (a) 3; (b) 33