Prime Numbers from 1 - 10

A prime number is a natural number. It is greater than 1 and is divisible only by 1 and the number itself. Some important properties of prime numbers include:

1. A prime number is only divisible by 1 and itself. It has no other divisors.

2. The set of prime numbers is infinite; this means there is no largest prime number.

3. Every number greater than 1 is either a prime or is factored into prime numbers.

4. The frequency of prime numbers decreases with an increase in natural numbers.

5. Prime numbers do not occur in fixed patterns but can be determined using a set of rules.

A prime number chart visually represents prime numbers in ascending order. It helps identify prime numbers within a given range of natural numbers. The chart has color codes for prime and composite numbers making it easier for students to differentiate between them.

Some important observations that can be made from a prime number 1 - 10 chart are:

• The smallest and only even prime number is 2.

• All prime numbers after two are odd. This is because every even number is divisible by 2.

• As the natural numbers increase (1, 2 …, 1000), the appearance of consecutive prime numbers decreases.

The chart plays a significant role as an effective teaching tool. It helps educators by providing visual highlights of prime numbers, It also helps students with factoring and calculations.
 

There are 4 prime numbers between 1 and 10. These prime numbers are: 2, 3, 5, 7.

1 is not considered prime because it is only divisible by itself. A prime number must have exactly two divisors.

In order for a number to be prime, it must have only 2 divisors, 1 and the number itself. All even numbers greater than two are divisible by 2. So, 2 is the only even prime number. All other prime numbers are odd numbers.

To identify a prime number, we need to check the number of factors a natural number has. If only 1 and the number itself are its factors, then that number is a prime number. There are various methods to test for primality. Two commonly used methods are:

This method checks whether a number can be divided evenly without any remainders by divisors other than itself or 1. 
Steps to follow the divisibility method are:
Start by dividing the number by small prime numbers like 2, 3, 5, 7 up to the square root of the number.
If the number is divisible by any of the above, then it is not a prime number.
If these numbers are not the divisors, then the number is prime.
For example:
Question: Check if 4 is a prime number.
Answer: 4 is divisible by 2, so it is not a prime number.

This method factors the given number into prime factors. If the given number is a product of natural numbers other than 1 and itself, it is not a prime number.
Steps for finding prime numbers by the prime factorization method:
Try to break down the number into a multiplication of two prime factors..
If possible, it is a composite number.
If not, it is a prime number.
For example:
Question: Check if 9 is a prime number.
Answer: 9 = 3 × 3. Since it can be written as the product of its prime factors, 9 is not a prime number.

Learning how to find prime numbers becomes simpler by using a few rules. These rules help determine whether a number is prime or composite. Some of these rules are:

Rule 1: Divisibility check:

A prime number is a natural number greater than 1 that cannot be divided evenly by any number other than 1 and itself. To identify a prime number using the divisibility check, we test if it is divisible by smaller prime numbers like 2, 3, 5, or 7. If it is divisible by any of these, then it is not a prime.

Rule 2: Prime Factorization:

The prime factorization method checks if the number can be written as a product of its prime factors. If the prime factors include numbers other than itself and one, the number is composite.

Rule 3: Sieve of Eratosthenes Method:

Developed by Greek mathematician Eratosthenes, this is an ancient systematic method used to find all prime numbers within a certain limit. This method works by eliminating multiples of prime numbers, leaving only prime numbers.

• Memorize the four prime numbers 2, 3, 5, 7 between 1 - 10.

• 2 is the only even prime number.

• 1 is not a prime number.

• All digits ending in 2, 5, and 0 are not composite except for 2 and 5. This is because all digits ending in 2, 5, or 0 are divisible by 2 or 5, or both.

• Prime number: Prime numbers are natural numbers greater than 1 with exactly two positive divisors: 1 and itself. For example, 2, 3, 5, and 7 are all prime numbers.

• Composite numbers: Composite numbers are natural numbers greater than 1, having more than two positive divisors. For example, 4, 6, 8, and 9 are all composite numbers.

• Divisor: A divisor is a number that completely divides another number without leaving any remainder. It is also known as the factor of that number. For example, 2 is a divisor of 4.

• Even Number: Any number divisible by 2 is an even number. For example, 2, 4, 6, 8, 10.

• Odd number: Any number that is not divisible by 2 is odd. For example, 3, 5, 7, 9, 1, etc.

• Natural number: Counting numbers starting from 1 are all natural numbers. So 1, 2, 3, 4, 5, 6, 7, 8 … etc., are all natural numbers.