What are Even Numbers:
- Natural numbers of the form 2n are called even numbers.
- All even numbers are completely divisible by number 2. (remainder = 0 )
- 2, 4, 6, …
- Smallest even number is 2.
Odd Numbers:
- Natural numbers of the form 2n -1 are called odd numbers.
- Smallest odd number is 1
- 1, 3, 5....
Note -
- All Natural Numbers are whole numbers.
- All Whole Numbers are Integers.
- All Integers are Rational Numbers.
- All Rational Numbers are Real Numbers.
Prime Numbers:
- The natural numbers greater than 1 which are divisible by 1 and the number itself are called prime numbers.
- Prime numbers have two factors i.e., 1 and the number itself . Example- 2, 3, 5, 7 & 11 etc.
- 1 is not a prime number as it has only one factor.
What are the Prime Numbers from 1 to 100?
There are 25 prime numbers up to 100. These prime numbers from 1 to 100 are listed as follows: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Composite Numbers:
- The natural numbers which are divisible by 1, itself and any other number or numbers are called composite numbers.
- For example, 4, 6, 8, 9, 10 etc.
Note: 1 is neither prime nor a composite number.
List of Composite Numbers Between 1 to 100
There is a total of 74 composite numbers from 1 to 100. The list of composite numbers between 1 to 100 includes 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, and 100. All other numbers between 1 and 100 except these are prime numbers.
Odd Composite Numbers 1 to 100
Odd composite numbers mean all the numbers that are not prime. For example, 63, 55, 69, and so on. There are a total of 25 odd composite numbers from 1 to 100. The list of odd composite numbers 1 to 100 includes 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99.
Even Composite Numbers From 1 to 100
Even composite numbers are even numbers that have more than two factors. As we know, all even numbers except 2 are composite. So, all even numbers except 2 between 1 to 100 are composite numbers. So, the list of even composite numbers from 1 to 100 are 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70,72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, and 100.
Co-prime Numbers:
- Co-prime numbers are pairs of numbers that do not have any common factor other than 1.
- There should be a minimum of two numbers to form a set of co-prime numbers. Such numbers have only 1 as their highest common factor, for example, (4 and 7), (5, 7, 9) are co-prime numbers.
- It is to be noted that co-prime numbers need not be prime numbers always.
- Two composite numbers like 4 and 9 also form a pair of co-primes.
Properties of Co-prime Numbers
Co-prime numbers can be identified easily with the help of some properties that are explained below:
The Highest Common Factor (HCF) of two co-prime numbers is always 1. For example, 5 and 9 are coprime numbers, there, HCF (5, 9) = 1.
The Least Common Multiple (LCM) of two co-primes is always their product. For example, 5 and 9 are co-prime numbers. Hence, LCM (5, 9) = 45.
1 forms a co-prime number pair with every number.
Two cannot be co-prime numbers as they always have 2 as the common factor.
The sum of two co-prime numbers is always co-prime with their product. For example, 5 and 9 are co-prime numbers. Here, 5 + 9 = 14 is co-prime with 5 × 9 = 45.
Two prime numbers are always co-prime. They have only 1 as their common factor. Consider 29 and 31. 29 has 2 prime factors, 1 and 29 only. 31 has 2 prime factors, 1 and 31 only. 29 and 31 are prime numbers. They have only one common factor 1. Thus they are co-prime. We can check any two prime numbers and get them as co-prime. For example, 2 and 3, 5 and 7, 11 and 13, and so on.
All pairs of two consecutive numbers are co-prime numbers. Any two consecutive numbers have 1 as their common factor.
Consider a few pairs of such numbers. Let us try with 14 and 15.
| Numbers | 14 | 15 |
|---|---|---|
| Factors | 1,2,7,14 | 1,3,5,15 |
| Common Factor | 1 |
There are multiple such combinations where 1 is the only common factor.
Co-prime and Twin Prime Numbers
Co-prime numbers are those numbers whose HCF is 1.Twin prime numbers are those prime numbers whose difference is always 2.For example, 3 and 5 are twin prime numbers.
The following points list the difference between co-prime and twin prime numbers.
Twin prime numbers are always prime numbers while co-prime numbers can be composite numbers as well.
The difference between two twin primes is always 2 while the difference between two co-primes can be any number.
All the pairs of twin prime numbers are also co-prime, while all co-prime numbers may or may not be twin primes.
1 forms a co-prime pair with every number, while it forms twin prime pair with only 3.
Important Notes
- Two numbers are co-prime if their GCF is 1. It can also be said that if the GCF of any two numbers is 1, those are co-prime numbers.
- Co-prime numbers need not necessarily be prime numbers. For example, 12 and 35 are co-prime numbers, although, 12 and 35 are NOT prime numbers.
Tips and Tricks:
- Any two prime numbers are always co-prime.
- Any two consecutive numbers are always co-prime.
- 1 forms a co-prime pair with any other number.
- A prime number is co-prime with any other number that is not its multiple.
- Two even numbers are NEVER co-prime.