Is 1094 a Prime Number?

Numbers can be categorized as

either prime numbers or composite numbers, depending on the number of factors they have.

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 only 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 possess certain properties:

• 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 1094 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1094 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including: 

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

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of divisors, we classify numbers accordingly: - If there is a total count of only 2 divisors, the number is prime. - If the count is more than 2, the number is composite. Let's check whether 1094 is prime or composite.

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

Step 2: Divide 1094 by 2. It is divisible by 2, so 2 is a factor of 1094.

Step 3: Divide 1094 by 3. It is not divisible by 3, so 3 is not a factor of 1094.

Step 4: You can simplify checking divisors up to 1094 by finding the square root value. We only need to check divisors up to the root value.

Step 5: When we divide 1094 by 2, 547, and other numbers, it is divisible by 2 and 547.

Since 1094 has more than 2 divisors, it is a composite number.

The divisibility test method involves using a set of rules to check whether a number is divisible by another number completely. Here are some example tests:

Divisibility by 2: The number in the ones' place value is 4, which is even, meaning that 1094 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1094 is 14. Since 14 is not divisible by 3, 1094 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 1094 is not divisible by 5. 

Divisibility by 7: Using the divisibility rule for 7, we find that 1094 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is not divisible by 11, so 1094 is not divisible by 11.

Since 1094 is divisible by more than just 1 and itself, it is a composite number.

A prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” This method involves:

Step 1: Writing numbers from 1 to 1000 in rows and columns.

Step 2: Leaving 1 unmarked since it is neither prime nor composite.

Step 3: Marking 2 as a prime number and crossing out all multiples of 2.

Step 4: Marking 3 as a prime number and crossing out all multiples of 3.

Step 5: Continuing the process until reaching 1000 to have a list of prime numbers. Since

  1094 is not present in the list of prime numbers, it is a composite number.

Prime factorization involves breaking down a number into its prime factors and multiplying those factors to obtain the original number.

Step 1: We can write 1094 as 2 × 547.

Step 2: Both 2 and 547 are prime numbers.

Step 3: The prime factorization of 1094 is 2 × 547.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.
   
• Divisibility rules: Rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 2 if its last digit is even.
   
• Sieve of Eratosthenes: An algorithm to find all prime numbers up to a specified integer. It involves marking the multiples of each prime number starting from 2.
   
• Co-prime numbers: Two numbers that have only one common factor, which is 1. For example, 8 and 15 are co-prime numbers.