Is 953 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 that is 1.
   
• As 953 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 953 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

• 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 either 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 953 is prime or composite.

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

Step 2: Divide 953 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 953 by 3. The sum of the digits (9 + 5 + 3 = 17) is not divisible by 3, so it is not divisible by 3.

Step 4: Continue checking divisibility by prime numbers up to the square root of 953, which is approximately 30.88, so check divisibility up to 29.

After checking divisibility by prime numbers such as 5, 7, 11, 13, 17, 19, 23, and 29, you will find that 953 is divisible by 7 (953 ÷ 7 = 136.14).

Since 953 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. This is called the Divisibility Test Method.

Divisibility by 2: 953 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 953 is 17. Since 17 is not divisible by 3, 953 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3, so 953 is not divisible by 5. 

Divisibility by 7: By applying the divisibility rule for 7, we find that 953 ÷ 7 = 136.14, indicating that 953 is divisible by 7. 

Divisibility by 11: The alternating sum of the digits (9 - 5 + 3 = 7) is not divisible by 11, so 953 is not divisible by 11.

Since 953 is divisible by 7, 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 from 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 until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we have a list of prime numbers.

Since 953 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 and then multiplying those factors to obtain the original number.

Step 1: Begin with the smallest prime number, 2. Since 953 is odd, it is not divisible by 2.

Step 2: Check for divisibility by primes up to the square root of 953.

Step 3: After checking, we find 953 is divisible by 7 (953 ÷ 7 = 136.14).

Hence, the prime factorization of 953 involves the factors 7 and other non-prime factors.

• 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 Numbers: Numbers greater than 1 that have no other divisors apart from 1 and themselves. 
   
• Divisibility: The ability for one number to be divided by another without leaving a remainder. 
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.
   
• Divisibility Rules: A set of rules that help determine if one number is divisible by another.