Question

A teacher shared 250 pencils and 350 books between the students each student gets equal amounts of pencils and books what is the maximum number of students

Answer 1

to find the maximum number of students who can receive equal amounts of both pencils and books, we need to determine the greatest common divisor (GCD) of the given quantities of pencils and books.

Explanation:

The GCD will represent the largest number of students who can receive an equal distribution of pencils and books. Let's solve this step by step:

Step 1: List the quantities of pencils and books:

Pencils: 250

Books: 350

Step 2: Find the GCD of the quantities:

The GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder.

We can use the Euclidean algorithm to find the GCD:

Divide the larger number by the smaller number: 350 ÷ 250 = 1 with a remainder of 100.

Now, divide the smaller number (250) by the remainder (100): 250 ÷ 100 = 2 with a remainder of 50.

Divide the remainder (100) by the new remainder (50): 100 ÷ 50 = 2 with no remainder.

Since we've reached a remainder of 0, the last non-zero remainder (50) is the GCD.

Step 3: Calculate the maximum number of students:

Since the GCD represents the largest number of students who can receive an equal distribution of both pencils and books, the maximum number of students is 50.

Explanation: The GCD of 250 and 350 is 50. This means that the given quantities of pencils and books can be evenly distributed among 50 students, with each student receiving the same number of pencils and books.

So, the maximum number of students who can receive equal amounts of both pencils and books is 5.

Answer 2

50 students is the maximum

Explanation:

We need the Highest Common Factor of 250 and 350

250 = 2*5*5*5

350 = 2*5*5*7

The HCF is 2*5*5

= 50.

So 50 pupils each get 5 pencils and 7 books for maximum number of students.