Is 1356 a Prime Number?

Numbers can be classified as prime or composite based 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 by 1 and itself only.

A composite number has more than two factors. For instance, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Here are some properties of prime numbers:

• Prime numbers are always greater than 1 and are positive.
  
   
• 2 is the only even prime number.
  
   
• They have exactly two factors: 1 and the number itself.
  
   
• Any two distinct prime numbers are coprime because they only share the factor 1.
   

Since 1356 has more than two factors, it is not a prime number.

A prime number is characterized by having exactly two divisors: 1 and itself. Since 1356 has more than two factors, it is not a prime number. Various methods can be used to distinguish between prime and composite numbers, such as:

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

The counting divisors method involves counting the number of divisors a number has to determine if it is prime or composite.

If there are only 2 divisors, the number is prime.

If there are more than 2 divisors, the number is composite.

Let’s determine if 1356 is prime or composite.

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

Step 2: Divide 1356 by 2. It is divisible by 2, so 2 is a factor of 1356.

Step 3: Divide 1356 by 3. The sum of the digits (1 + 3 + 5 + 6 = 15) is divisible by 3, so 3 is also a factor of 1356.

Step 4: Continue checking divisibility with other numbers up to the square root of 1356.

Since 1356 has more than 2 divisors, it is a composite number.

The Divisibility Test Method involves using rules to determine if a number is completely divisible by another number:

Divisibility by 2: The last digit of 1356 is 6, an even number, so 1356 is divisible by 2.

Divisibility by 3: The sum of the digits (1 + 3 + 5 + 6 = 15) is divisible by 3, so 1356 is also divisible by 3.

Divisibility by 5: The last digit is not 0 or 5, so 1356 is not divisible by 5.

Divisibility by 7: Doubling the last digit (6 × 2 = 12) and subtracting from the rest of the number (135 - 12 = 123) gives a number divisible by 7, so 1356 is divisible by 7.

Divisibility by 11: Alternating sum and difference of digits (1 - 3 + 5 - 6 = -3) is not divisible by 11, so 1356 is not divisible by 11.

Since 1356 ha

s multiple divisors, it is a composite number.

A prime number chart can be constructed using a method like the Sieve of Eratosthenes:

Step 1: Write numbers from 1 to 100 (or more) in a grid.

Step 2: Leave 1 unmarked as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out all multiples of 2.

Step 4: Mark the next uncrossed number, 3, as prime and cross out its multiples.

Step 5: Continue this process for subsequent numbers.

Since 1356 is not found in the list of prime numbers, it is a composite number.

Prime factorization involves breaking a number down into its prime factors:

Step 1: Begin with the smallest prime number, 2. Divide 1356 by 2 to get 678.

Step 2: 678 is also divisible by 2, giving 339.

Step 3: 339 is divisible by 3, yielding 113.

Step 4: 113 is a prime number.

Thus, the prime factorization of 1356 is 2 × 2 × 3 × 113.

• Composite numbers: Numbers greater than 1 that have more than two factors. For example, 1356 is composite because it has multiple factors.
  
   
• Prime numbers: Numbers greater than 1 with exactly two distinct factors: 1 and the number itself. For example, 113 is a prime number.
  
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, 1, 2, and 3 are factors of 6.
  
   
• Divisibility rules: Guidelines to determine if one number is divisible by another without performing the division.
  
   
• 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.