Explain Integers and Prime Numbers

integers and prime numbers

What are Integers?

The word integer is developed and termed from the Latin word “Integer” which explains something as a whole and entire. Integers are an original set and consist of whole numbers that include zero, positive numbers, and negative numbers represented on the number line. Integers are expressed by the capital letter Z. Examples of Integers – 1, 77, 15.

Rules of Integers

The foundational and primary rules for integers are stated below:

  • The Sum of two particular positive integers is without exception an integer
  • The Sum of two given negative integers is without exception an integer
  • The product of two given positive integers is without exception an integer
  • The product of two given negative integers is without exception an integer
  • The Sum of an integer and its respective inverse is without exception equal to zero
  • The product of an integer and its reciprocal is without exception equal to 1

Properties of Integers

The most primary and vital characteristics of Integers are stated below:

  • Closure Property
  • Associative Property
  • Commutative Property
  • Distributive Property
  • Additive Inverse Property
  • Multiplicative Inverse Property
  • Identity Property

What are Prime Numbers?

Prime numbers are those positive integers that include only two factors that are the number 1 and the integer itself in an original set. For instance, the factors of 8 are 1,2,4, and 8, there are four factors in total, but factors of 2 are only the number 1 and 2. Hence, 2 is a positive prime number but the number 8 is not, instead, it matches all the properties of a composite and natural number.

It is vital and important to invariably remember that the number 1 is neither a prime number nor a composite number. There is no expressed or standard formula for finding a prime number, apart from knowing its respective factors in the number system. If X is a prime, then it’s only and existing factors are 1 and X itself. Any particular number which does not follow this property of operation is known as composite numbers, which means that they can be factored into other comprehensive positive integers.

History of Prime Numbers

The prime number was termed and explained by Eratosthenes, Greece. He took the example of a sieve to filter out the prime numbers from a list of all-natural numbers on the number line and then drained them out of all the composite numbers from the original number set. Students can practice this method, by listing all the positive integers from 1 to 100 in a number line and then circling the prime numbers, finally then putting a hyphen to chuck out all existing composite numbers.

Properties of Prime Numbers

Some of the fundamental characteristics of prime numbers are stated below:

  • Every number greater than 1 is divided by one prime number in the number line.
  • Every even positive integer greater than number 2 can be processed as the sum of two primes.
  • Except 2, all other prime numbers in the number line are odd numbers. In other words, we can say that 2 is the only existing even prime number in the number system.
  • Two given prime numbers are always coprime to each other in the number line.

Is 1 a Prime Number?

Let us refer to the explanation of the prime numbers, which states that a number should have accurately only two factors for it to be called a prime number. But, 1 has only one factor which is number 1 itself. Consecutively, number 1 is not considered as a prime number.

Examples: 2, 3, 5, 7, 17, and much more. In all the positive integers existing in the number system, all are either divisible by number 1 or itself, that is precisely only two positive integers in the whole of the number system.

I hope you had fun exploring integers and prime numbers. With online learning platforms like Cuemath, you can explore prime numbers in the most unique and interesting ways. Cuemath uses visual tools to help students understand the concept of prime numbers and integers that makes learning super fun and engaging. Happy Learning!