There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers have a few properties, such as:

• Prime numbers are positive numbers always greater than 1.
   
• 2 is the only even prime number.
   
• They have only two factors: 1 and the number itself
  .
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
   
• As 1071 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1071 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. A few methods are:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. If there is a total count of only 2 divisors, then the number would be prime. If the count is more than 2, then the number is composite. Let’s check whether 1071 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 1071 by 2. It is not divisible by 2, so 2 is not a factor of 1071.

Step 3: Divide 1071 by 3. It is divisible by 3, so 3 is a factor of 1071.

Step 4: You can simplify checking divisors up to 1071 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1071 by 3, 7, and 11, it is divisible by 3 and 7.

Since 1071 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 1, an odd number, so 1071 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1071 is 9. Since 9 is divisible by 3, 1071 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 1071 is not divisible by 5.

Divisibility by 7: Doubling the last digit (1 × 2 = 2) and subtracting from the rest (107 - 2 = 105), 105 is divisible by 7, so 1071 is divisible by 7.

Divisibility by 11: The alternating sum of digits (1 - 0 + 7 - 1) is 7, which is not divisible by 11. Thus, 1071 is not divisible by 11. Since 1071 is divisible by 3 and 7, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write numbers in a systematic manner, such as from 1 to 100 or more.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until the chart is filled with marked and crossed numbers, except 1. Through this process, we will have a list of prime numbers.

Since 1071 is not in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 1071 as 3 × 357.

Step 2: In 3 × 357, 357 is a composite number. Further, break 357 into 3 × 119.

Step 3: Now, break 119 into 7 × 17.

Step 4: The prime factorization of 1071 is 3 × 3 × 7 × 17.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. Examples include 2, 3, 5, etc.

• Divisibility rules: A set of rules that help determine whether a given number is divisible by another without performing division.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.