To find the largest number of bouquets without having any flowers left over, we need to find the greatest common divisor (GCD) of 36, 27, and 28.
The prime factorization of 36 is 2^2 * 3^2, thus its factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The prime factorization of 27 is 3^3, thus its factors are 1, 3, 9, and 27.
The prime factorization of 28 is 2^2 * 7, thus its factors are 1, 2, 4, 7, 14, and 28.
The common factors among these numbers are 1 and 9. Therefore, the largest number of bouquets she can make without having any flowers left over is 9.
