Question: A school is distributing candies and pencils to students. The school has 120 candies and 180 pencils, and it wants to divide them equally among students such that each student gets the same number of candies and pencils. What is the maximum number of students that the school can divide the items among?
(A) 20 students
(B) 30 students
(C) 40 students
(D) 60 students
Solution:
We need to find the HCF of 120 and 180.
Prime factorization of 120:
120=2³×3×5
Prime factorization of 180:
180=2²×3²×5
HCF is the product of the lowest powers of all common prime factors:
HCF(120,180)= 2²×3×5=4×3×5=60
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