For a number to be prime it must only have factors of one and itself.

10 has factors 1, 2, 5, 10.

15 has factors 1, 3, 5, 15.

18 has factors 1, 2, 3, 6, 9, 18.

The only factors of 13 are 1 and 13. As such it is prime.

Irrational numbers are defined by the fact that they cannot be written as a fraction which means that the decimals continue forever. 

Looking at our possible answer choices we see,

 is already in fraction form

 which is an imaginary number but still rational.

Therefore since,

we can conclude it is irrational.

An irrational number is a number that cannot be written in fraction form. In other words a nonrepeating decimal is an irrational number.

The  is an irrational number. 

 is a real number with a value of .

Therefore, . This is a real but irrational number.

The graph shown never intersects with the x-axis. This means that the x-intercepts must be imaginary.

The square root of 5 is irrational since it is a non-terminating, non-repeating decimal that cannot be expressed as a fraction.

 A rational number is a number that can be expressed in the form p/q. in this case p=3 and q=1. The other answers are irrational because they cannot be expressed as whole numbers or fractions.

Step 1: Define the different sets:

Rational: Any number that can be expressed as a fraction (improper/proper form) (example: )
Irrational: Any number whose decimal expansion cannot be written as a fraction. (example: )
Real numbers: The combination of all numbers that belong in the Rational and the Irrational set.  (Example: )
Integers: All whole numbers from . (Example: )
Natural Numbers (AKA Counting numbers): All numbers greater than or equal to 1, 

Step 2: Let's categorize the numbers given in the question to these sets above:

 belongs to the set of rational numbers, natural numbers, and integers.
 belongs to the set of rational numbers and integers.
 belongs to the set of rational numbers.

Step 3: Analyze each number closely and pull out any sets where all three numbers belong..

All three numbers belong to the set of rational numbers.

In math, we symbolize rational numbers as .
So, all three numbers belong to the sets .

The definition of natural numbers states that the number may not be negative, and must be countable where:

Decimal places and fractions are also not allowed.

The value of fifty percent equates to .

The only possible answer is:  

Natural numbers are numbers can be countable.  Natural numbers cannot be negative.  They are whole numbers which include zero.

The fraction given is not a natural number.

Notice that the imaginary term  can be reduced.  Recall that , and .  This means that .

The answer is:  

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set -  - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.