Prime numbers are positive whole numbers which are divisible by number 1 and itself. Prime numbers have only two factors. The smallest prime number is 2. Now the question arises is 1 a prime number? No, 1 is not a prime number. So our next question will be why 1 is not a prime number? As per the definition of prime numbers, a prime number must have two factors but 1 only has one factor. It is the only positive integer with exactly one positive divisor. Therefore it is not considered as a prime number.
Is 2 a prime number? 2 is a prime number as it is divisible by 1 and itself. It has two factors and as per the definition of a prime number, prime number must have two factors. Therefore, 2 is considered as a prime number and it is the only even number which is considered as prime. The other prime numbers are divisible by 2 also so they do not come under a category of a prime number.
Euclid proved that there are infinite prime numbers and there is always a prime greater than the largest known prime number. Many mathematicians tried finding out the largest prime number. The largest prime number found in 2008 was 2^43112609-1
Let us learn about relatively prime numbers. Two numbers that have only 1 as a common factor are called relatively prime numbers. Thus, any two prime numbers are relatively prime numbers. They are also called co prime numbers. However, composite numbers may also be co - prime to each other.
For example: - Numbers 3375 and 2744 are considered as relatively prime because:-
3375 = 1 X 3 X 3 X 3 X 5 X 5 X5
2744 = 1 X 2 X 2 X 2 X 7 X 7 X 7
3375 and 2744 have just 1 as a common factor so they are considered as relatively prime numbers.
Is 2 a prime number? 2 is a prime number as it is divisible by 1 and itself. It has two factors and as per the definition of a prime number, prime number must have two factors. Therefore, 2 is considered as a prime number and it is the only even number which is considered as prime. The other prime numbers are divisible by 2 also so they do not come under a category of a prime number.
Euclid proved that there are infinite prime numbers and there is always a prime greater than the largest known prime number. Many mathematicians tried finding out the largest prime number. The largest prime number found in 2008 was 2^43112609-1
Let us learn about relatively prime numbers. Two numbers that have only 1 as a common factor are called relatively prime numbers. Thus, any two prime numbers are relatively prime numbers. They are also called co prime numbers. However, composite numbers may also be co - prime to each other.
For example: - Numbers 3375 and 2744 are considered as relatively prime because:-
3375 = 1 X 3 X 3 X 3 X 5 X 5 X5
2744 = 1 X 2 X 2 X 2 X 7 X 7 X 7
3375 and 2744 have just 1 as a common factor so they are considered as relatively prime numbers.
