In mathematics, the number which produces greater than 1 and this number has exactly two factors, namely 1 and the number itself. This type of number is called the prime number and can also be called as the primary numbers.
The number which produces greater than 1 is labeled as a composite number and this composite number has minimum of three factors, namely 1, the number itself and one other factor.
Therefore, the number 1 is a neither prime nor composite number.
Primary Numbers up to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
Primary numbers greater than 100:
Let ‘ x’ be a given number greater than100. To determine whether it is prime number or composite number, we use the following method:
Calculate a whole number approximately greater than the square root of ‘x’.
Let `y >sqrt(x)` , test whether ‘ x’ is divisible by any prime number less than y. If yes, then ‘x’ is a composite number otherwise, ‘x’ is prime number.
Between, if you have problem on these topics what are relatively prime numbers, please browse expert math related websites for more help on Practice Math Problems.
Primary Numbers – Example 1:
Check whether the given number is a primary numbers or not.
(a). 443.
Solution:
Given:
443.
Steps for checking the primary numbers of 443:
Step 1: We have to find whether the number 443 is a prime or composite number.
Step 2: Let `22 >sqrt(443)` .
Step 3: Prime numbers of below 22 are, 2, 3, 5, 7, 11,13, 17, and 19.
Step 4: We check whether the number 443 is divisible by any one of them.
Here,
` (443)/(2)` => 443 are not divisible by 2.
` (443)/(3)` => 443 are not divisible by 3.
`(443)/(5)` => 443 are not divisible by 5.
`(443)/(7)` => 443 are not divisible by 7.
`(443)/(11)` => 443 are not divisible by 11.
`(443)/(13)` => 443 are not divisible by 13.
`(443)/(17)` => 443 are not divisible by 17.
`(443)/(19)` => 443 are not divisible by 19.
Step 5: That is, the given number 443 is not divided by any of them. Therefore, the given number 443 is a primary numbers.
Primary Numbers – Example 2:
Check whether the given number is a primary numbers or not.
(a). 344.
Solution:
Given:
344.
Steps for checking the primary numbers of 344:
Step 1: We have to find whether the number 344 is a prime or composite number.
Step 2: Let `19 >sqrt(344)` .
Step 3: Prime numbers of below 19 are, 2, 3, 5, 7, 11,13, and 17.
Step 4: We check whether the number 344 is divisible by any one of them.
Here,
` (344)/(2)` => 172.
` (344)/(3)` => 344 are not divisible by 3.
`(344)/(5)` => 344 are not divisible by 5.
`(344)/(7)` => 344 are not divisible by 7.
`(344)/(11)` => 344 are not divisible by 11.
`(344)/(13)` => 344 are not divisible by 13.
`(344)/(17)` => 344 are not divisible by 17.
Step 5: That is, the given number 344 is divided by the primary number 2. Therefore, the given number 344 is not a primary numbers and also it can be clled composite number.
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