The number of people at the theatre when rounded to the nearest hundred was 3400.

1. Determine the least possible number that rounds to 3400 to the nearest hundred

When rounding to the nearest hundred, the number must be at least $3400 - 50 = 3350$. Any number from $3350$ to $3399$ rounds up to $3400$. Therefore, the least possible number is $3350$.

1. Determine the upper bound for rounding to the nearest hundred

When rounding to the nearest hundred, numbers from $3350$ up to $3449$ round to $3400$.

2. Identify the greatest possible integer

Since the number of people must be a whole number, the greatest possible value is $3449$.