По известному процессу деления в столбик найти частное (то есть найти пропущенные цифры):
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 7\) | \(\displaystyle 1\) | \(\displaystyle 4\) | ||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle 0\) |
Найдем пропущенные цифры при делении в столбик:
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 7\) | \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle {\small?}\) | \(\displaystyle {\small?}\) | \(\displaystyle {\small?}\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle 0\) |
1. Под \(\displaystyle 730\) стоит число \(\displaystyle 714={\bf 3}\cdot 238{\small.}\) Следовательно, первая неизвестная цифра частного – это \(\displaystyle 3{\small:}\)
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle \bf 7\) | \(\displaystyle \bf 1\) | \(\displaystyle \bf 4\) | \(\displaystyle \bf 3\) | \(\displaystyle {\small?}\) | \(\displaystyle {\small?}\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle 0\) |
2. Далее вычитаем из \(\displaystyle 730\) число \(\displaystyle 714\) (\(\displaystyle 730-714=16\)) и сносим цифру из разряда десятков числа \(\displaystyle 730{\bf6}6\) (это цифра \(\displaystyle 6\)). Получаем число \(\displaystyle 166{\small.}\)
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 7\) | \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 3\) | \(\displaystyle {\small?}\) | \(\displaystyle {\small?}\) | |||
| \(\displaystyle \bf 1\) | \(\displaystyle \bf 6\) | \(\displaystyle \bf 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle 0\) |
Число \(\displaystyle 166\) меньше \(\displaystyle 238{\small,}\) поэтому сносим следующий разряд (то есть единицы числа \(\displaystyle 7306{\bf6}{\small,}\)) и записываем \(\displaystyle {\bf 0}\) в частном. Поэтому вторая неизвестная цифра частного – это \(\displaystyle 0{\small.}\)
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 7\) | \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle {\small?}\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle 0\) |
3. Под числом \(\displaystyle 1666\) стоит число \(\displaystyle 1666{\small.}\) Чтобы получить число \(\displaystyle 1666{\small,}\) надо \(\displaystyle 238\) умножить на \(\displaystyle 7\) (\(\displaystyle 1666=238\cdot {\bf 7} \)). Следовательно, третья неизвестная цифра частного – это \(\displaystyle 7{\small.}\)
| \(\displaystyle 7\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 3\) | \(\displaystyle 8\) | |
| \(\displaystyle –\) | ||||||||
| \(\displaystyle 7\) | \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle \bf 7\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | \(\displaystyle 6\) | \(\displaystyle 6\) | |||||
| \(\displaystyle –\) | ||||||||
| \(\displaystyle \bf 1\) | \(\displaystyle \bf 6\) | \(\displaystyle \bf 6\) | \(\displaystyle \bf 6\) | |||||
| \(\displaystyle 0\) |
Ответ: \(\displaystyle 307{\small.}\)