state fundamental theorem of arithmetic.
Answers
Step-by-step explanation:
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors. For example,
1200 = 24 × 31 × 52 = 2 × 2 × 2 × 2 × 3 × 5 × 5 = 5 × 2 × 5 × 2 × 3 × 2 × 2 = ...
The theorem says two things for this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product.
The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (e.g., 12 = 2 × 6 = 3 × 4).
This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique;
hope it helps
Answer:
Fundamental theorem of arithmetic
" The law states that every composite number can be factorized as the product of primes and this factorisation is unique apart from the order in which the factors comes "
It also means that composite number greater than 1 could be factorized as a unique product of prime numbers
Take the case of number 1176
Prime Factorization of 1176 = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7
This means that every composite number could be shown as a factors of primes.
for instance , 4 = 2*2
8 = 2 * 2* 2
20 = 5 * 2 * 2
70 = 7 * 5* 2
etc,