Even number: number divisible by 2

Prime number: is a natural number greater than 1 that has only two factors (1 and the number itself).

2 is an even number because it can divide itself to obtain 1 and it is also a prime number because no other number can divide it except 1 and itself.

Integers

These are the set of all whole numbers but it includes a negative set of natural numbers also. Hence whole numbers and natural numbers are subsets of set of integers. "Z" represents integers and the set of integers include, Z = {...,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,...}

Prime number is a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11)

To express a number as a product of prime factors express the number as a multiple of prime numbers and simplify in a form of indexes

108 = 2 x 54

108 = 2 x 2 x 27

108 = 2 x 2 x 3 x 9

108 = 2 x 2 x 3 x 3 x 3

Now apply the law of indexes

a^m x aⁿ = a^{m + n}

Thus if the bases are the same and are multiplying, you can add the powers

a = a¹

Thus every number is raised to the power 1

108 = 2 x 2 x 3 x 3 x 3 = 2¹ x 2¹ x 3¹ x 3¹ x 3¹

108 = 2¹⁺¹ x 3¹⁺¹⁺¹

108 = 2² x 3³