7. In one school library, there are 24850 books, and in another - 55300. When these books were being arranged on shelves equally, 154 books were left in the first library, and 175 in the other. How many books were placed on each shelf?
7. The desired number is a common divisor of the numbers $24696(24850-154=24696)$ and $55125(55300-175=55125)$. Since $24696=2^{3} \cdot 3^{2} \cdot 7^{3}$ and $55125=3^{2} \cdot 5^{3} \cdot 7^{2}$, the common divisors are $3,7,9,21,49,63,147,441$. Since the divisor must be greater than the remainder, only 441 satisfies the condition of the problem. Therefore, 441 books were placed on each shelf.