735. Find the greatest divisor of the pair of numbers 123456789 and 987654321 (in other words, the greatest common measure of segments of such lengths).
$\triangleright$ In principle, this problem can be solved by brute force (and even in a reasonable time if you have a computer at hand), trying all numbers from 1 to 123456789 (larger numbers clearly do not fit).

However, it can also be done without a computer, using the Euclidean algorithm. The number 987654321 can be replaced by $987654321-123456789=864197532$. Subtracting 123456789 again, we get 740740743, then 617283954, 493827165, 370370376, 246913587, 123456798, and finally, $123456798-123456789=9$. (In the end, we divided 987654321 by 123456789 with a remainder and got a remainder of 9.) As we have seen, the common divisors of the original pair and the pair 123456789, 9 are the same, and according to the Euclidean algorithm, we need to subtract 9 from 123456789. The number 123456789 is divisible by 9 (it equals $9 \cdot 13717421$), so when subtracting, we get 9 (and then 0). Answer: the greatest common divisor is $9. \triangleleft$