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in Mathematics by (76.5k points)

What is the sum of the digits of the smallest positive integer which is divisible by 99 and has all of its digits equal to 2 ?

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As number is divisible 99

 it should be divisible by 9 and 11.

for divisibility by 9 the sum of digit is divisible by 9. As the number contains only 2 as digit so the sum of digit should be 18, 36,....... But the number should be divisible by 11 so we can’t take sum as 18. So we take sum of digit is 36. So required number = 2222........... up to 18 times. Which is divisible by 11 and 9 i.e., 99.

Sum of the digits = 36.

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