Is 951 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 951 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 951 has more than two factors, it is not a prime number. A 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 951 is prime or composite.

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

Step 2: Divide 951 by 2. It is not divisible by 2, so 2 is not a factor of 951.

Step 3: Divide 951 by 3. Since 9+5+1=15 and 15 is divisible by 3, 951 is divisible by 3, making 3 a factor.

Step 4: Check divisors up to the square root of 951, which is approximately 30.8.

Step 5: After checking, 951 is also divisible by 9 (951/9 = 105.666...).

Since 951 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's called the Divisibility Test Method. 

Divisibility by 3: The sum of the digits in 951 is 15. Since 15 is divisible by 3, 951 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 1, which means 951 is not divisible by 5.

Divisibility by 7: Double the last digit (1 × 2 = 2). Subtract it from the rest of the number (95 - 2 = 93). Check if 93 is divisible by 7. Since 93 is not divisible by 7, 951 is not divisible by 7. 

Divisibility by 11: 9 - 5 + 1 = 5. Since 5 is not divisible by 11, 951 is not divisible by 11.

Since 951 is divisible by 3, 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 these steps:

Step 1: Write numbers up to 1000 in rows and columns.

Step 2: Leave 1 without marking, 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. Through this process, we obtain a list of prime numbers. 951 is not on the list, making it 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 951 as 3 × 317.

Step 2: Check if 317 is a prime number. As 317 is not divisible by any prime numbers up to its square root, it remains a prime number.

Step 3: Therefore, the prime factorization of 951 is 3 × 317.

• 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.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.
   
• Divisibility Rules: Guidelines that help determine whether a number is divisible by another number without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime Numbers: Two numbers that have only 1 as their common factor.