Is 955 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 a 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, which is 1.
   
• As 955 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 955 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, such as: 

• 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 955 is prime or composite.

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

Step 2: Divide 955 by 2. It is not divisible by 2, so 2 is not a factor of 955.

Step 3: Divide 955 by 3. The sum of the digits is 19, which is not divisible by 3.

Step 4: Divide 955 by 5. The last digit is not 0 or 5, so 955 is not divisible by 5.

Step 5: Divide 955 by 7. 955 divided by 7 gives a remainder, so 955 is not divisible by 7. Continue this process up to √955, which is approximately 30.9. After testing, it is found that 955 is divisible by 5 and 191.

Since 955 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: 955 is not divisible by 2 because it is odd.

Divisibility by 3: The sum of the digits in 955 is 19. Since 19 is not divisible by 3, 955 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 955 is divisible by 5. 

Divisibility by 7: Dividing 955 by 7 does not result in a whole number, so it is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is 11, which is divisible by 11, meaning 955 is divisible by 11.

Since 955 is divisible by numbers other than 1 and itself, 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 range, such as 1 to 1000, in rows and 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 up to the square root of the largest number in your chart.

Through this process, we will have a list of prime numbers from 1 to 1000. Since 955 is not present in the list of prime numbers, it is a composite number.

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 955 as 5 × 191.

Step 2: Both 5 and 191 are prime numbers.

Hence, the prime factorization of 955 is 5 × 191.

• 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.
   
• Divisibility Rules: Guidelines to quickly determine if a number is divisible by another without performing the full division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. 
   
• Prime Factorization: Expressing a number as a product of its prime numbers.
   
• Co-prime numbers: Two numbers that have only one common factor, which is 1.