Is 1059 a Prime Number?

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 certain 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 1059 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 1059 has more than two factors, it is not a prime number. Several 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 numbers as prime or composite. - 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 1059 is prime or composite.

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

Step 2: Divide 1059 by 2. It is not divisible by 2, so 2 is not a factor of 1059.

Step 3: Divide 1059 by 3. The sum of the digits is 15 (1+0+5+9), which is divisible by 3, so 3 is a factor of 1059.

Step 4: Continue checking divisors up to the square root of 1059.

Step 5: When we divide 1059 by 3, 9, and other factors, we find that it is divisible by these numbers.

Since 1059 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 is 9, which is odd. Therefore, 1059 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1059 is 15, which is divisible by 3. Hence, 1059 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 9, so 1059 is not divisible by 5. 

Divisibility by 7: Doubling the last digit (9 × 2 = 18) and subtracting it from the rest (105 - 18 = 87), 87 is divisible by 3 but not by 7. 

Divisibility by 11: The difference between the sum of the digits in odd positions (1 + 5 = 6) and even positions (0 + 9 = 9) is 3, which is not divisible by 11.

Since 1059 is divisible by 3, it has more than two factors, making it 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 grid.

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 up to a reasonable number to identify prime numbers.

Since 1059 is not found in the list of prime numbers identified, 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 1059 as 3 × 353.

Step 2: Check if 353 is a prime number.

Step 3: It turns out 353 is a prime number, so the prime factorization of 1059 is 3 × 353.

•  Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1059 is a composite number because it is divisible by 1, 3, 353, and 1059. 2.

• Prime factorization: The process of breaking down a number into a product of its prime factors. 3.

• Divisibility rules: Simple rules used to determine whether a number is divisible by another number without performing division. 4.

• Co-prime numbers: Two numbers that have only one common factor, which is 1. 5.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.