Fundamental theorem of arithmetic :-

Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique . apart from the other in which factors occur.

The fundamental theorem of arithmetic or the unique factorisation theorem would fail.

The prime factorisation theorem is also known as the fundamental theorem of arithmetic. So in that context, it does.

Because otherwise the fundamental theorem of arithmetic, the unique factorisation theorem, would fail.

The fundamental theorem of arithmetic states that every integer greater than 1 is either a prime number or can be written as a product of prime numbers. In the latter case, the prime numbers are uniquely determined apart from the order in which they appear.

The theorem is also known as the unique prime factorisation theorem - for obvious reasons.

The fundamental theorem of arithmetic says any integer can be factored into a unique product of primes. The is the prime factored form.

It is the prime factorisation of the number which, due to the fundamental theorem of arithmetic, is unique.

The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.

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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

The Fundamental theorem of arithmetic.

The most important concept is that, apart from their order, the prime factorisation of any number is unique. This is known as the Fundamental Theorem of Arithmetic.

look in google if not there, look in wikipedia.

fundamental theorem of algebra and their proofs

math and arithmetic

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 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

Prime factorizations are unique. If you change the prime factorization, you change the number.

According to the Fundamental Theorem of Arithmetic, there is only one way to write the prime factors of any integer which is greater than 1.

Neither.

According t the fundamental theorem of arithmetic (also called the unique prime factorisation theorem), any integer has one and only one prime factorisation.

In any case, both numbers have 4 prime factors.

Yes. The Fundamental Theorem of Arithmetic states that every composite number has one and only one prime factorization; the above is one expression of this fact.

If you were to factor 21, you would get its factors to be 7 and 3. When you multiply these numbers you will get back to 21. This is a result of the Fundamental theorem of arithmetic.

You can read more at:

http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

It is neither because the property of prime or composite is defined only for integers which are 2 or larger. The underlying reason is to ensure that the prime factorisation theorem (the fundamental theorem of arithmetic) remains valid.

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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

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They are the fundamental operations of arithmetic: addition, subtraction, multiplication and division.

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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

Carl Friedrich Gauss...

He is responsible for the FTC, or fundamental theorem of calculus.

Mathematics begins with arithmetic.

cause your fat. ;)

The four fundamental operations in arithmetic are addition, subtraction, multiplication and division.

1 is evenly divisible only by 1 and itself (also 1). In that respect it is like a prime. However, if 1 were a prime then the Fundamental Theorem of Arithmetic - the Unique Prime Factorisation Theorem would fail - and with it much of arithmetic would become invalid.

The Fundamental Theorem of Arithmetic states that there is a unique factorisation for any integer - up to the order of the factors. This means that for any number the list of its factors and their multiplicities is unique. That statement is no longer true if 1 is considered to be a prime.

168

12,14

2,6,14

2,2,3,14

2,2,2,3,7

Algebra is used for mathematics

Writing a number as a product of its prime factors is called prime factorization. Any number greater than 1 can be written as a unique product of its prime factors.This is called the Fundamental Theorem of Arithmetic.

We need more information. Is there a limit or integral? The theorem states that the deivitive of an integral of a function is the function

Because the property of being a prime or composite is defined only for numbers which are two or larger. If 1 were considered a prime then the fundamental theorem of arithmetic - the unique prime factorisation theorem - would fail.

The Liouville theorem states that every bounded entire function must be constant and the consequences of which are that it proves the fundamental proof of Algebra.

The fundamental operations are operations in arithmetic: addition, subtraction, multiplication and division. These are the same whatever the base of the number system.

Malthusian theorem is a population projection that suggests the population will exceed the available food supply because populations grow at geometric rates, while food supplies grow at arithmetic rates

Thanks to the fundamental theorem of arithmetic, there can be only one prime factorisation (leaving aside the factor 1), for ANY integer. As a result, there is only one prime factorisation of 30 and so nothing for it to be different from!

Because the concept of prime or composite is defined for whole numbers which are greater than 1. 1 is not divisible by any number except for 1 and itself (also 1). From that perspective, it should be classed as a prime. However, if 1 were considered a prime than the fundamental theorem of arithmetic - the unique prime factorisation theorem - would fail, and with it much of the theory of multiplication and division would collapse.

The Weierstrass theorem is significant in mathematical analysis because it guarantees the existence of continuous functions that approximate any given function on a closed interval. This theorem is fundamental in understanding the behavior of functions and their approximation in calculus and analysis.

If, by trigonometry theorem you mean the "fundamental theorem of trigonometry," sin2(x) + cos2(x) = 1, it is actually the Pythagorean Theorem. if you have a right triangle with a hypotenuse of one, sin(x) is one leg, and cos(x) is the other. The Pythagorean Theorem states that a2 + b2 = c2 and therefore sin2(x) + cos2(x) = 1.

I am not sure there are any fundamental operations of integers. The fundamental operations of arithmetic are addition, subtraction, multiplication and division. However, the set of integers is not closed with respect to division: that is, the division of one integer by another does not necessarily result in an integer.

the longest string of prime factor for 30 is 2 x 3 x 5

An Arithmetic logic unit (ALU) is a digital circuit that performs arithmetic and logical operations. The ALU is a fundamental building block of the central processing unit (CPU) of a computer, and even the simplest microprocessors contain one for purposes such as maintaining timers.

Because the Fundamental Theorem of Arithmetic specifies that every integer greater than 1 has its own unique prime factorization, it is impossible to specify what each of these prime factorizations is, however, it is true that the prime factorization of every even number includes the number 2 as the lowest prime factor.