The middle school band has 56 members. the high school band has 96 members. the bands are going to march one after another in a parade. the director wants the arrange the bands into thre same number of columns. what is the greatest number of columns in which the two bands can be arranged if each column has the same number of marchers? how many band members will me in each column

it depends on how many people he wants in each column .

Both numbers are divisible by 2.
but he wants the greatest number of columns we try 4 and it works we try 8 and it works we try 16 and it does not ! so the maximum number of columns that satisfies both numbers is 8
so both bands can be divided by 8 columns .
the high school band will have 8 columns having 12 marchers each while the middle school one will have 8 columns having 7 marchers each
12x8=96 ,7x8=56