Question

The head of a conference wants to distribute the male and female staff members evenly among all the check-in stations, with no staff members left over. If there are 30 male and 75 female staff members, what is the greatest number of check-in stations that can be set up?

• A. 150
• B. 5
• C. 15
• D. 30

Answer 1

The correct option is C 15

Greatest common divisor of 30 and 75 is the greatest number of check-in stations that can be set up

Prime factorisation of 30 and 75:
$30=2\times \underset{–}{3}\times \underset{–}{5}$
$75=\underset{–}{3}\times \underset{–}{5}\times 5$

The common factors of 30 and 75 are 3 and 5, so the greatest common divisor of 30 and 75 is $3\times 5=\underset{–}{15}.$

That means that the greatest possible number of check-in stations is 15, because 30 male staff members can be hired at 15 stations with 2 males each and 75 female staff members can be hired at 15 stations with 5 females each.

The greatest number of check-in stations that can be set up is 15.