Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
Question:
Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
Answer:
Let's think step by step.

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Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
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