When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the…
When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?
15713
15723
15783
15873
Solution
We need the smallest repunit (number made of all 1's) divisible by 7. Checking 1, 11, 111, 1111, 11111 - none divisible by 7; 111111 is divisible by 7. So the number is $111111 \div 7 = 15873$. Verification: $15873 \times 7 = 111111$.