1. The problem is to explain how 48 marbles can be shared into different equal groups. 2. To share marbles into equal groups, we need to find the divisors of 48. Each divisor represents a possible group size where the marbles can be evenly divided. 3. The formula to check if a number $d$ is a divisor of 48 is: $$48 \div d = \text{an integer}$$ 4. Let's find all divisors of 48 by testing numbers from 1 to 48: - $48 \div 1 = 48$ (integer) - $48 \div 2 = 24$ (integer) - $48 \div 3 = 16$ (integer) - $48 \div 4 = 12$ (integer) - $48 \div 6 = 8$ (integer) - $48 \div 8 = 6$ (integer) - $48 \div 12 = 4$ (integer) - $48 \div 16 = 3$ (integer) - $48 \div 24 = 2$ (integer) - $48 \div 48 = 1$ (integer) 5. These divisors mean the marbles can be shared into groups of sizes 1, 2, 3, 4, 6, 8, 12, 16, 24, or 48, with each group having an equal number of marbles. 6. For example, if we choose groups of 6 marbles, there will be $48 \div 6 = 8$ groups. 7. This method ensures all marbles are shared equally without any leftover. Final answer: The 48 marbles can be shared into equal groups of sizes 1, 2, 3, 4, 6, 8, 12, 16, 24, or 48.