VTMO 2026 - Grade 6 - Semifinal - SET 1 - Self-study Question 24

Let $A=\{1,11,111,\ldots,\underbrace{11\ldots1}_{35\text{ digits}},\underbrace{11\ldots1}_{36\text{ digits}}\}$. How many elements of $A$ divide the number consisting of 36 digits, all equal to 1?