Gina buys one pack of each colour and makes bunches of balloons to hand out. She splits each pack evenly across the bunches. What is the greatest number of bunches she can make if she uses all the balloons?
To maximize the number of bunches, Gina needs to divide the balloons into the smallest possible number of groups. The number of bunches she can make is equal to the greatest common divisor (GCD) of the number of balloons of each color.
If Gina buys one pack of each color, she has a total of 5 + 6 + 7 = <<5+6+7=18>>18 balloons.
The GCD of 5, 6, and 7 is 1 (since none of the numbers have a common factor).
Therefore, Gina can make a maximum of 1 bunch if she uses all the balloons.