Euclid’s division algorithm
Any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.
Fundamental Theorem of Arithmetic
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Two main applications.
First, we use it to prove the irrationality of many of the numbers, such as √2, √3, and √5 .
Second, we apply this theorem to explore when exactly the decimal expansion of a rational number, say p/q (q ≠ 0) , is terminating and when it is non-terminating repeating.
- Real numbers yield a positive result when squared