A composite number is: a whole number that can be divided evenly by numbers other than 1 or itself.
Because every even number is divisible by #2# all of the even numbers between 31 and 53 are part of the solution set for this problem:
#32, 34, 36, 38, 40, 42, 44, 46, 48. 50, 52#
Every number ending with #5# is evenly divisible by #5# so we can add these numbers to the solution set:
#32, 34, color(red)(35), 36, 38, 40, 42, 44, color(red)(45), 46, 48. 50, 52#
This leaves:
#33, 37, 39, 41, 43, 47, 49, 51#
The digits in #33#, #39# and #51# are evenly divisible by #3# so we can add them to the solution set:
#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. 50, color(blue)(51), 52#
This leaves:
#37, 41, 43, 47, 49#
#49# is #7^2# so this can be added to the solution set:
#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. color(orange)(49), 50, color(blue)(51), 52#
This leaves: #37, 41, 43, 47# These are all prime numbers and therefore not composite numbers so the solution is:
#32, color(blue)(33), 34, color(red)(35), 36, 38, color(blue)(39), 40, 42, 44, color(red)(45), 46, 48. color(orange)(49), 50, color(blue)(51), 52#