The expression "quotient of 27" seems slightly grammatically incorrect and ambiguous without a context.
When we divide one number by another, it may give an exact result, or may be expressed as a quotient and remainder.
For example:
192 / 7 = 27 with remainder 3
The number 192 is called the dividend
The number 7 is the divisor
The number 27 is the quotient
The number 3 is the remainder
So you might say in this example: "When dividing 192 by 7 you get a quotient of 27 and remainder 3". The word "of" here is not really needed or correct.
When we divide 27 by another whole number, it can only give an exact result if the divisor is a factor of 27. You could use the expression "quotient of 27" to mean any possible result of such a division. An example might be: "When dividing numbers by 3 the quotient of 27 is 9.". This seems slightly cumbersome.
A better example would be "What is the quotient of 27 divided by 3?". In this question "quotient of 27" is not a noun in itself, the question is asking "What is the quotient when you divide 27 by 3?"
