A certain number of chocolates which is a perfect square are distributed among 2156 students of a school equally. Find the minimum number of chocolates distributed given that it is greater than 90,000.94864984649986496864
Question
A certain number of chocolates which is a perfect square are distributed among 2156 students of a school equally. Find the minimum number of chocolates distributed given that it is greater than 90,000.94864984649986496864
Solution
The problem is asking for the minimum number of chocolates that can be distributed among 2156 students, where the number of chocolates is a perfect square and is greater than 90,000.
Step 1: Find the smallest perfect square greater than 90,000.
The square root of 90,000 is approximately 300. Therefore, the smallest perfect square greater than 90,000 is 301^2 = 90601.
Step 2: Check if this number can be evenly distributed among 2156 students.
90601 divided by 2156 is approximately 42.01. This is not an integer, so 90601 chocolates cannot be evenly distributed among the students.
Step 3: Find the next perfect square.
The next perfect square is 302^2 = 91204.
Step 4: Check if this number can be evenly distributed among 2156 students.
91204 divided by 2156 is approximately 42.29. This is not an integer, so 91204 chocolates cannot be evenly distributed among the students.
Step 5: Continue this process until you find a perfect square that can be evenly distributed among 2156 students.
After trying a few more perfect squares, you will find that 316^2 = 99856 can be evenly distributed among 2156 students, because 99856 divided by 2156 equals 46.
Therefore, the minimum number of chocolates that can be distributed among 2156 students, where the number of chocolates is a perfect square and is greater than 90,000, is 99856.
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