1. Разложите на простые множители число: а) 88; б) 528; в) 1836; г) 7128.

Решение:

1. а) 88
   88 = 2 ⋅ 44 = 2 ⋅ 2 ⋅ 22 = 2 ⋅ 2 ⋅ 2 ⋅ 11 = 2³ ⋅ 11.
2. б) 528
   528 = 2 ⋅ 264 = 2 ⋅ 2 ⋅ 132 = 2 ⋅ 2 ⋅ 2 ⋅ 66 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 33 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 11 = 2⁴ ⋅ 3 ⋅ 11.
3. в) 1836
   1836 = 2 ⋅ 918 = 2 ⋅ 2 ⋅ 459 = 2 ⋅ 2 ⋅ 3 ⋅ 153 = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 51 = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 17 = 2² ⋅ 3³ ⋅ 17.
4. г) 7128
   7128 = 2 ⋅ 3564 = 2 ⋅ 2 ⋅ 1782 = 2 ⋅ 2 ⋅ 2 ⋅ 891 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 297 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 99 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 33 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 11 = 2³ ⋅ 3⁴ ⋅ 11.

Ответ: а) 2³ ⋅ 11; б) 2⁴ ⋅ 3 ⋅ 11; в) 2² ⋅ 3³ ⋅ 17; г) 2³ ⋅ 3⁴ ⋅ 11.