Final answer:
The greatest number of bags Hallie can make without any leftovers is 6, which is the greatest common divisor of 12 friendship bracelets and 54 erasers.
Step-by-step explanation:
To find the greatest number of bags that Hallie can make without having any items left over, we need to determine the greatest common divisor (GCD) of the two numbers in question, which are 12 friendship bracelets and 54 erasers.
The GCD is the largest number that will divide both 12 and 54 without any remainder.
When we list down the factors of 12, we have 1, 2, 3, 4, 6, and 12.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors of 12 and 54 are 1, 2, 3, and 6.
Among these, the greatest common factor is 6.
Therefore, Hallie can make 6 bags with an equal number of friendship bracelets and erasers in each, which would be 2 bracelets and 9 erasers per bag, since dividing 12 bracelets by 6 gives 2 bracelets per bag, and dividing 54 erasers by 6 gives 9 erasers per bag.