# What is a quotient of 27?

Sep 20, 2015

Depending on the context, it could mean:

(1) The result of dividing $27$ by another number.
(2) That $27$ is the result of dividing one number by another.

#### Explanation:

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:

$\frac{192}{7} = 27$ 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 $3$?"