Answer:
1) 13 and 31, 17 and 71, 79 and 97
2)a. 7 × 20 = 5(20) + 2(20)
b. 7 × 25 = 5(25) + 2(25)
c. 72 × 7 = (80 - 8)(10 - 3)
d. 78 × 11 = (80 - 2)(10 + 1)
3) 102 is divisible by 3 and 6, but not by 18.
4) Sum of factors of
18: 1 + 2 + 3 + 6 + 9 = 21
20: 1 + 2 + 4 + 5 + 10 = 22
24: 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36
30: 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42
36: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55
18, 20, 24, 30, and 36 are abundant
numbers.
5) 65 = 7² + 4² = 8² + 1²
85 = 7² + 6² = 9² + 2²
6) a. 73 = 4³ + 2³ + 1³ = 64 + 8 + 1
b. 92 = 4³ + 3³ + 1³ = 64 + 27 + 1
c. 99 = 4³ + 3³ + 2³ = 64 + 27 + 8
7) a. 1³ + 2³ = (1 + 2)²
b. 1³ + 2³ + 3³ = (1 + 2 + 3)²