Find the maximum number of students among whom 1003 chocolates and 2703 candies can be distributed such that each student gets the same number of each.

a) 19
b) 29
c) 17
d) 33

Ans : 17

Solution

Let’s find the HCF of 1003 and 2703:

Prime Factorization Method:

Factorize 1003 and 2703 to their prime factors.

• 1003=17×59 (Both 17 and 59 are prime numbers)
• 2703=3×17×53 (Here, 3, 17, and 53 are prime numbers)

Finding the HCF / GCD:

The common factor between 1003 and 2703 is 17.

Hence, the HCF is 17.

Thus, the maximum number of students among whom 1003 chocolates and 2703 candies can be distributed equally is 17.