Question

state the fundamental theorem of arithmetic and Euclid division Lemma

Answer 1

Answer

The Fundamental Theorem of Arithmetic

Any integer greater than one either is a prime or itself can be represented as a product of prime numbers. The representation is unique.

Example number 20 can be represented as,

20 = 2 x 2 x 5

Euclid division Lemma

Consider positive integers, a, b, q and r,

If we divide a by b, the quotient is q and remainder is r such that r< b

we can write a = bq + r

This is called Euclid division Lemma

example let a= 20, b=3

20 = 3 x 6 + 2

q=6 and r= 2 r<q

Answer 2

Answer:

Step-by-step explanation:

FUNDAMENTAL THEOREM OF ARITHMETIC :  

According to the fundamental theorem of arithmetic every composite number can be written or  factorized as the product of primes and this factorization is unique, apart from the order in which the prime factors occur.  

Fundamental theorem of arithmetic , is also called, UNIQUE FACTORIZATION THEOREM.

Composite number =  product of prime numbers

Or  

Any integer greater than one, either be a prime number or can be written as a product of prime factors.

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