0
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1[note 1] either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.[3][4][5] For example,
1200 = 24 × 31 × 52 = 3 × 2 × 2 × 2 × 2 × 5 × 5 = 5 × 2 × 3 × 2 × 5 × 2 × 2 = etc.
The theorem is stating two things: first, that 1200 canbe represented as a product of primes, and second, no matter how this is done, there will always be 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 for which 1 is not considered as a Prime number: if 1 were prime, the factorization would not be unique, as, for example, 2 = 2×1 = 2×1×1 = ...
Wiki User
∙ 8y ago
Add your answer:
Earn +20 pts
Why is one a prime number?
One is not a prime number. A prime number, by definition, is a number that is only divisible by two numbers: one and itself. One is divisible by only one number, one, and therefore is not a prime number.
Is the number one a prime factor?
No 1 it is not a prime number. The definition of a prime number is that it can only have factors of one and itself. Since one already has one then it can not be a prime number.
What is one if it is not a prime number?
one is in fact a prime number.
Why prime number prime?
A prime number is a number that has only two factors which are itself and one
What is the one prime even number?
2 is one prime even number.
Why is is important that 1 is not a prime number?
It important that 1 is not prime because a quote says: "A prime number is a natural number that has exactly two different natural number factors. and so i say 1 is not a prime because a prime number has 2 factor 1 and it self and 1 dose not.
What number has only one prime factor?
No prime number only has one factor. Each prime number has itself and 1 as factors. Now, the number 1 of course has only one factor, but it is technically not a prime number.
With a given big integer number which is the product of two prime numbers how do you find them?
First write a program to generate the prime number. After one prime number was generated, divide the big int number by the prime number. If the remainder is zero then quotient is the second prime number ( also it is important to check whether the quotient is prime number or not because sometimes you will get wrong answer). Repeat the process until you get the result.
What is it called when a number can only be divided by one and itself?
a prime number.
Why prime number prime?
A prime number is a number that has only two factors which are itself and one
Why will your opponent get atlest one point if you circle a prime number?
A prime number only has two factors: itself and the number one. You get the prime number, your opponent gets one.
Is one a perfect number?
no, but I don't know why. One is not a prime number and by definition of a perfect number one must be a prime number.
Does every prime number have one even prime number?
No. The only even prime number is 2.
Is 3 a prime or composite or neither?
3 is a prime number. Any number that only has itself and one as factors is a prime number. Therefore, since there are no factors of 3 other than one and itself it is a prime number.
Is it possible for a squared number to be prime?
No, a prime number is only divisible by itself and one. And since one doesn't count as a prime number, no.
What has one factor and is not a prime number?
It is 1 which is neither a prime nor a composite number
What are prime number and composite numbers?
a prime number is a number that you can plus by one
