The Fundamental Theorem of Arithmetic

Let us start with the definition:

Any integer greater than 1 is either a prime number, or can be written as a unique product of prime numbers (ignoring the order).

Simply:  Every number greater than 1 can be expressed as the product of primes in a unique way except for the order in which the factors appear.

Just like this Example:
72 = 2 * 2 * 2 * 3 * 3
  
Greatest Common Divisor
The Greatest Common Divisor (GCD) of two or more numbers is a (unique) number.

1. which is a factor of each of the numbers that it is a common factor of all the numbers and
2. which is greatest among the common factors of these numbers.

Example:

• Factors of 12 are 1,2,3,4,6 and 12.
• Factors of 16 are 1,2,4,8 and 16.
• Here, common factors are 1,2, and 4. Out of these, 4 is the greatest. Therefore, the GCD of 12 and 16 is 4.