The cafeteria has 144 bananas, 36 pears, and 72 apples. Each student gets the same number of pieces of fruit. What is the greatest number of students who can receive fruit?
The 48 members of a chorus will sit in rows in front of the 300 members of the audience. All the rows have the same number of chairs. What is the greatest possible number of chairs in each row?
1. We need to find the greatest common divisor. IT might be 36. We check : 36/36 =1 , 72/36 = 2, 144/36 = 4
So the greatest number of students who can receive fruit is 36 (each student gets 1,2,4 fruits respectively)
2. Hmm...I'm sorta confused about this question...are the 48 members in the rows along with the 300 members?
exmples of logarithms
To find the greatest number of students who can receive fruit, we need to find the greatest common divisor (GCD) of the given quantities of bananas, pears, and apples. The GCD represents the largest number that divides all the quantities without leaving a remainder.
For this problem, we can use the prime factorization method to determine the GCD. Calculate the prime factors of each quantity:
- Bananas = 2² * 3² * 5
- Pears = 2² * 3²
- Apples = 2³ * 3²
Next, find the common prime factors for all three quantities:
- Common prime factors = 2² * 3² = 36
Therefore, the greatest number of students who can receive fruit is 36.
Similarly, to find the greatest possible number of chairs in each row, we need to find the GCD of the number of members in the chorus and the number of members in the audience.
Let's calculate the GCD using the prime factorization method:
- Chorus members = 2³ * 3 = 24
- Audience members = 2² * 3 * 5² = 300
The common prime factors are 2² * 3 = 12.
Therefore, the greatest possible number of chairs in each row is 12.