Chapter 15 (Number Theory - Part 26 ) Topic : Fundamental Theorem of Arithmetic (FTA) (Part 2)

Fundamental Theorem of Arithmetic (FTA):

The Fundamental Theorem of Arithmetic is one of the most important theorems in Number Theory.

Statement:
Every integer greater than 1 can be expressed as a product of prime numbers in one and only one way (except for the order of the factors).

Example: 12=2×2×3

We cannot write 12 as a product of different prime factors.

Why Is It Important?
Because almost every Number Theory concept depends on prime factorization.
Using prime factorization we can find:
• HCF (GCD)
• LCM
• Number of divisors
• Sum of divisors
• Euler's Totient Function
• Perfect squares and cubes
• Divisibility tests

Key Points to Remember:

✅ The factorization is unique (except order).
✅ Prime numbers are the "building blocks" of all integers.
✅ FTA is the foundation of Number Theory.

One-Line Summary:
Fundamental Theorem of Arithmetic: Every integer greater than 1 has a unique prime factorization.

Видео Chapter 15 (Number Theory - Part 26 ) Topic : Fundamental Theorem of Arithmetic (FTA) (Part 2) канала Math Olympiad by Golam Minhaz