2.14 Разложите на простые множители числа: a) 108, 225, 270, 512, 945, 1024; б) 90, 180, 270, 350, 450, 1350, 4500; B) 13, 2002, 1225, 14014, 90 720.

a) 108 = 2 * 2 * 3 * 3 * 3; 225 = 3 * 3 * 5 * 5; 270 = 2 * 3 * 3 * 3 * 5; 512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2; 945 = 3 * 3 * 3 * 5 * 7; 1024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

б) 90 = 2 * 3 * 3 * 5; 180 = 2 * 2 * 3 * 3 * 5; 270 = 2 * 3 * 3 * 3 * 5; 350 = 2 * 5 * 5 * 7; 450 = 2 * 3 * 3 * 5 * 5; 1350 = 2 * 3 * 3 * 3 * 5 * 5; 4500 = 2 * 2 * 3 * 3 * 5 * 5 * 5

в) 13 = 13; 2002 = 2 * 7 * 11 * 13; 1225 = 5 * 5 * 7 * 7; 14014 = 2 * 7 * 17 * 59; 90720 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 5 * 7

Ответ: a) 108 = 2² * 3³; 225 = 3² * 5²; 270 = 2 * 3³ * 5; 512 = 2⁹; 945 = 3³ * 5 * 7; 1024 = 2¹⁰; б) 90 = 2 * 3² * 5; 180 = 2² * 3² * 5; 270 = 2 * 3³ * 5; 350 = 2 * 5² * 7; 450 = 2 * 3² * 5²; 1350 = 2 * 3³ * 5²; 4500 = 2² * 3² * 5³; в) 13 = 13; 2002 = 2 * 7 * 11 * 13; 1225 = 5² * 7²; 14014 = 2 * 7 * 17 * 59; 90720 = 2⁶ * 3³ * 5 * 7