Organizer of school graduation does have three sections of chairs. 1120 chairs are arranged for graduates, 1400 for invited guests and 896 for lecturers. If all rows have same number of chairs, calculate the greatest number of chairs in each row if no chairs are left over? Calculate the number of rows in each sections.
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To calculate the greatest number of chairs in each row without any chairs being left over, we need to find the greatest common divisor (GCD) of the number of chairs in each section.
Let's calculate the GCD of the number of chairs in each section:
For graduates: 1120 chairs
For invited guests: 1400 chairs
For lecturers: 896 chairs
Now, we can find the GCD by prime factorizing each number:
1120 = 2^5 * 5 * 7
1400 = 2^3 * 5^2 * 7
896 = 2^7 * 7
Now, we can calculate the GCD by taking the smallest exponent for each prime factor:
GCD = 2^3 * 5^1 * 7^1 = 280
Therefore, the greatest number of chairs in each row without any chairs being left over is 280.
To calculate the number of rows in each section, we divide the total number of chairs in each section by the greatest number of chairs in each row.
For graduates: 1120 chairs / 280 chairs per row = 4 rows
For invited guests: 1400 chairs / 280 chairs per row = 5 rows
For lecturers: 896 chairs / 280 chairs per row = 3 rows
Therefore, there are 4 rows for graduates, 5 rows for invited guests, and 3 rows for lecturers.