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 follow few properties like

• 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 that is 1.
   
• As 1057 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 1057 has more than two factors, it is not a prime number. Few methods are 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 1057 is prime or composite.

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

Step 2: Divide 1057 by 2. It is not divisible by 2, so 2 is not a factor of 1057.

Step 3: Divide 1057 by 3. The sum of the digits is 13, which is not divisible by 3, so 3 is not a factor.

Step 4: You can simplify checking divisors up to 1057 by finding the root value. We then need to only check divisors up to the root value (approximately 32.5).

Step 5: Continue checking divisibility by 5, 7, 11, 13, and so on up to 32.

After testing various divisors, 1057 is found to be divisible by 7 and 151, showing it has more than 2 divisors, making it 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: 1057 is odd, so not divisible by 2.

Divisibility by 3: The sum of the digits in 1057 is 13. Since 13 is not divisible by 3, 1057 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1057 is not divisible by 5.

Divisibility by 7: Applying the divisibility rule for 7, 1057 is divisible by 7.

Divisibility by 11: Alternating sum of the digits is 1 - 0 + 5 - 7 = -1, which is not divisible by 11.

Since 1057 is divisible by 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 1 to 100 in 10 rows and 10 columns.

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 you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

As 1057 is not in the range of 1 to 100, additional checks are needed, which show 1057 is not prime as it is divisible by 7.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 1057 as 7 × 151.

Step 2: Both 7 and 151 are prime numbers.

Step 3: The prime factorization of 1057 is therefore 7 × 151.

• 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.

• 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.

• Divisibility: A concept of dividing a number by another number to see if the dividend is divisible without leaving a remainder.

• Prime number: A natural number greater than 1 that is not divisible by any number other than 1 and itself.

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