Задача: 37376373 × 837737
Цель: понять детальное решение.
Пошаговое решение:
1) Разделим второе число: 837737 = 837000 + 737.
Тогда A × 837737 = A × 837000 + A × 737, где A = 37376373.
2) Вычислим A × 837000:
A × 837000 = (A × 837) × 1000.
3) Найдём A × 837 = A × (800 + 37) = A × 800 + A × 37.
- A × 800 = A × 8 × 100.
A × 8 = 37376373 × 8 = 299010984.
=> A × 800 = 299010984 × 100 = 29,901,098,400.
- A × 37 = A × (30 + 7) = A × 30 + A × 7.
A × 30 = 37376373 × 30 = 1,121,291,190.
A × 7 = 37376373 × 7 = 261,634,611.
=> A × 37 = 1,121,291,190 + 261,634,611 = 1,382,925,801.
=> A × 837 = A × 800 + A × 37 = 29,901,098,400 + 1,382,925,801 = 31,284,024,201.
=> A × 837000 = 31,284,024,201 × 1000 = 31,284,024,201,000.
4) Вычислим A × 737 = A × (700 + 30 + 7):
- A × 700 = (A × 7) × 100. A × 7 = 261,634,611, so A × 700 = 26,163,461,100.
- A × 30 = 1,121,291,190 (как ранее).
- A × 7 = 261,634,611.
=> A × 737 = 26,163,461,100 + 1,121,291,190 + 261,634,611 = 27,546,386,901.
5) Сложим части:
A × 837737 = A × 837000 + A × 737 = 31,284,024,201,000 + 27,546,386,901
= 31,311,570,587,901.
Ответ: 31 311 570 587 901.
