Is 969 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 that is 1.

As 969 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 969 has more than two factors, it is not a prime number. 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 969 is prime or composite.

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

Step 2: Divide 969 by 3. It is divisible by 3, so 3 is a factor of 969.

Step 3: Check divisibility by other numbers up to the square root of 969.

Step 4: 969 is divisible by 3, 17, and 57.

Since 969 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: The number in the ones' place value is 9, which is odd. Therefore, 969 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 969 is 24. Since 24 is divisible by 3, 969 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 969 is not divisible by 5.

Divisibility by 7: The last digit in 969 is 9. Double the last digit (9 × 2 = 18), subtract it from the rest of the number (96 - 18 = 78). Since 78 is divisible by 7, 969 is divisible by 7.

Since 969 is divisible by 3, 7, and other numbers, 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 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 will have a list of prime numbers.

Since 969 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 969 as 3 × 323.

Step 2: Break 323 into 17 × 19, which are primes.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 969 is 3 × 17 × 19.

• 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. For example, the prime factorization of 60 is 2 × 2 × 3 × 5.
  
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing long division.
  
   
• Square root: A value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.