Is 977 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 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 977 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 977 has exactly two factors, it is a prime number. Several methods can be 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 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 977 is prime or composite.

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

Step 2: Check divisibility of 977 with numbers up to its square root, which is approximately 31.2.

Step 3: 977 is not divisible by any prime numbers up to 31 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31).

Since 977 has only 2 divisors, it is a prime 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: 977 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 977 is 23, which is not divisible by 3.

Divisibility by 5: 977 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 977 is not divisible by 7.

Divisibility by 11: Alternating sum of the digits is 11, which is not divisible by 11.

Since 977 is not divisible by any numbers other than 1 and itself, it is a prime 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 1 to 1000 in a grid.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

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

Step 4: Mark 3 as prime and cross out all the multiples of 3.

Step 5: Repeat this process for prime numbers up to the square root of the largest number in the chart. Through this process, we will have a list of prime numbers.

977 is not crossed out, indicating it is a prime number.

Prime factorization is the process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: Attempt to divide 977 by the smallest prime number, 2. 977 is not divisible by 2.

Step 2: Check divisibility by the next prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

Step 3: 977 is not divisible by any of these primes.

Since 977 cannot be factored into other primes, it is a prime number.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.
  
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.
  
   
• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division.
  
   
• Sieve of Eratosthenes: A method to find all prime numbers up to a certain limit by iteratively marking the multiples of each prime number.
  
   
• Prime factorization: Breaking down a number into the product of its prime factors.