72 = 2³ × 3². Number of divisors = (3+1)(2+1) = 4 × 3 = 12.

Digit sum = 9 + 9 + 9 + 9 = 36. Note: A number and its digit sum have the same remainder when divided by 9.

6^x ÷ 216 = 6. 216 = 6³. So 6^x ÷ 6³ = 6. Therefore 6^(x-3) = 6¹. Thus x - 3 = 1, so x = 4.

Sum of first n natural numbers = n(n+1)/2. For n=15: 15×16/2 = 240/2 = 120

12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 4×9 = 36

For divisibility by 6, number must be divisible by both 2 and 3. 104÷6 = 17.33... (not divisible). Others: 72, 84, 90 are all divisible by 6

Let the number be x. According to the problem: 5x - 3 = 47. Therefore, 5x = 50, so x = 10.

12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.

We need to find x where x² = 169. Taking square root: x = √169 = 13.

We need a number of the form 8k + 5. Check: 29 = 8(3) + 5 = 24 + 5. ✓