## Task 4 - 070724

On an excursion, exactly 319 students traveled by buses, and on another excursion, exactly 232. In each of the buses that were used in total, the same number of students sat.

Determine this number! (We assume that more than one student sat in each bus.)
The number of students per bus must be a common divisor $>1$ of 319 and 232. Since $319=11 \cdot 29$ and $232=8 \cdot 29$, the prime number 29 is the only common divisor $>1$ of 319 and 232; because 11 and 8 are coprime.

Therefore, exactly 29 students traveled in each bus.

Solutions of the II. Round 1967 adopted from [5]

### 4.9.3 III. Round 1967, Class 7