Final answer:
The greatest number of groups that can be made is 7, with 3 pencils and 2 erasers in each group.
Step-by-step explanation:
To find the greatest number of groups that can be made so that each group has the same number of items, we need to find the greatest common divisor of 21 and 14, which is 7. So, the greatest number of groups is 7.
To calculate how many pencils will be in each group, we divide the total number of pencils (21) by the number of groups (7), giving us 3 pencils in each group.
To calculate how many erasers will be in each group, we divide the total number of erasers (14) by the number of groups (7), giving us 2 erasers in each group.