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Natural numbers as product of primes

natural numbers

Prime factorization is also known as unique-prime-factorization theorem. It states that any natural number greater than 1 or the prime number itself, can be obtained by the product of prime numbers. Any natural number n, can be obtained from the prime factors p1, p2, p3 ....pt. This is called as prime factorization.

For example,

6 = 3 x 2

72 = 2 x 2 x 2 x 3 x 3

42 = 2 x 3 x 7

8415 = 5 x 9 x 11 x 7

Any whole number can be created by multiplying the prime numbers greater than the one. So prime numbers are considered to be the building blocks of the natural numbers

Prime factorization is practically possible to work out for the large set of numbers. Euclids lemma is the fundamental proof for prime factorization. Euclid lemma states that if the prime numbers divides the property of two numbers, it must divide at least one of those numbers.

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