Is 959 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 959 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 959 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 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 959 is prime or composite.

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

- Step 2: Divide 959 by 2. It is not divisible by 2, so 2 is not a factor of 959.

- Step 3: Divide 959 by 3. It is not divisible by 3, so 3 is not a factor of 959.

- Step 4: Continue checking divisibility up to the square root of 959, which is approximately 31.

- Step 5: Upon checking, 959 is divisible by 7 (since 959 ÷ 7 = 137).

Since 959 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. Since 9 is an odd number, 959 is not divisible by 2.

- Divisibility by 3: The sum of the digits in the number 959 is 23. Since 23 is not divisible by 3, 959 is not divisible by 3.

- Divisibility by 5: The unit’s place digit is 9. Therefore, 959 is not divisible by 5.

- Divisibility by 7: Divide 959 by 7. Since 959 ÷ 7 = 137, it is divisible by 7.

Since 959 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 the following steps:

- Step 1: Write numbers in a sequence and systematically cross out the multiples of each prime number starting from 2.

- Step 2: Continue this process up to the square root of the highest number in the sequence. Through this process, we will have a list of prime numbers.

Since 959 is not found among these 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: We can write 959 as 7 × 137.

- Step 2: Both 7 and 137 are prime numbers.

Hence, the prime factorization of 959 is 7 × 137.

- Composite numbers: Natural numbers greater than 1 that have more than 2 factors. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.

 

- Prime numbers: Numbers greater than 1 that have no divisors other than 1 and itself. For example, 5 is a prime number because it can only be divided by 1 and 5.

 

- Divisibility rules: Rules that help determine if a number is divisible by another without performing full division.

- Prime factorization: The expression of a number as the product of its prime factors.

 

- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer by iteratively marking the multiples of each prime number starting from 2.