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#### Understanding The Prime Numbers And Examples

Referencing Styles : Harvard | Pages : 1

### Defining prime numbers:

The prime number or simply rime is a natural number which is greater than one. It can never be formed by multiplying two small natural numbers. Any natural number higher than one is never prime and is referred to as a composite number. Here, for instance, the number 5 can be taken. It is prime since it is the only method to write it as the product, 5*1 or 1*5 includes the number itself. Nevertheless, 6 is composite since this is the product of the two numbers 3*2 and are smaller than one. Infinitely many primes are there as referred by Euclid. There is no known simple formula that can separate the prime numbers from the composite ones. Nevertheless, the distribution of the rimes under natural numbers in large can be modelled statistically. In that direction, the initial outcomes of the “prime number theorem” that was proved during the 19th century. It states that the probability of the randomly chosen number to be prime has been inversely proportional to the number of the digits or its algorithm.

### Prime factorization:

The prime factorization is the process of finding which prime can multiply together in making the main number. Any number’s prime factorization is all the prime numbers that are multiplied in creating the original number.

### Ways to determine the prime factorization of any number:

Prime factorization can be determined through thinking about leaves in a tree. Here, the tree is the specific number. As it has broken down branches are created and the smallest factors are received and the leaves are seen. Here, the factor tree can be utilized as the process of performing prime factorization. Now, an example can be considered through the number 70. Various factors can be considered that provide the product 70. As it is even, it cam divisible by number two. 35*2 provides 70. 2 is a prime number and 35 is not a prime. Hence,the continuation is to be done. It is found out what provides the product of 35. 5*7=35 and it can be broken once again. Here, the numbers with which we are left can never be broken down any more. As only prime numbers are left, the prime factorization of 70 can be found looking at the leaves. 70’s prime factorization s 7*5*2. It is correct and it is known by the fact that the factors are multiplied to assure the result with the main value. 2*5=10 and 10*7=70.

Let the prime factorization of 147 is to be found.

147 ÷ 2 = 73½

As no whole number is not gained, the next prime number, 3 is to be tried.

147 ÷ 3 = 49

49 ÷ 7 = 7

147 = 3 × 7 × 7

Using exponents, 147 = 3 × 72

It must be reminded that it is the proper etiquette of math to write down the answer with prime values from the least to highest. It depends on how the original number is factored. Here some sort of rearranging is required.

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