A school wants to distribute 60 pencils and 75 erasers to students, such that all of them get an equal number of pencils and an equal number of erasers with no items left over. What is the maximum number of students who can receive this gift?
15
Every student must get the same whole number of pencils and the same whole number of erasers with nothing left over, so the number of students must divide both 60 and 75.
The largest such number is the HCF of 60 and 75.
60 = 22 × 3 × 5 and 75 = 3 × 52, so the HCF = 3 × 5 = 15.
With 15 students each gets 4 pencils and 5 erasers.
Hence, the answer is 15.
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