The local reader’s club has a set of 36 hardback books and a set of 30 paperbacks. Each set can be divided equally among the club members. What is the greatest possible number of club members? A. 5 B. 6 C. 30 D. 180
What is the greatest common factor of 30 and 36?
the greatest common factor of 30 and 36 is 6
Right, 6.
To find the greatest possible number of club members, we need to determine the greatest common divisor (GCD) of the total number of books in each set: 36 and 30.
One way to find the GCD is by listing the factors of each number and finding the largest common factor. Alternatively, we can use the Euclidean algorithm, which is a more efficient method for finding the GCD.
Using the Euclidean algorithm:
1. Divide the larger number (36) by the smaller number (30) and find the remainder: 36 ÷ 30 = 1 remainder 6.
2. Now, divide the previous divisor (30) by the remainder (6): 30 ÷ 6 = 5 remainder 0.
The remainder becomes zero, indicating that we have found the GCD. In this case, the GCD of 36 and 30 is 6.
The GCD, 6, represents the number of books that can be evenly divided among all the club members. To find the greatest possible number of club members, we divide the total number of books in each set by the GCD: 36 ÷ 6 = 6.
Therefore, the greatest possible number of club members is 6.
Hence, the correct answer is B. 6.