Problem 3. If we divide the numbers 701 and 592 by the same natural number, we get remainders of 8 and 7, respectively. By which number did we divide the given numbers?
Solution. The desired number is a common divisor of the numbers $701-8=693$ and $\quad 592-7=585$. Since $693=3 \cdot 3 \cdot 7 \cdot 11$ and $585=3 \cdot 3 \cdot 5 \cdot 13$, the common divisors are 1, 3, and $3 \cdot 3=9$. Since the divisor must be greater than the remainders, the desired divisor is the number 9.