Is 1195 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 1195 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 1195 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: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 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 1195 is prime or composite.

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

Step 2: Divide 1195 by 2. It is not divisible by 2, so 2 is not a factor of 1195.

Step 3: Divide 1195 by 3. It is not divisible by 3, so 3 is not a factor of 1195.

Step 4: You can simplify checking divisors up to 1195 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1195 by 5, it is divisible, so 5 is a factor.

Since 1195 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 5. Since 5 is an odd number, 1195 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1195 is 16. Since 16 is not divisible by 3, 1195 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 5. Therefore, 1195 is divisible by 5. 

Divisibility by 7: Perform a calculation using 1195 to check divisibility by 7. Since it doesn't divide evenly, 1195 is not divisible by 7. 

Divisibility by 11: In 1195, the alternating sum of the digits (1 - 1 + 9 - 5 = 4) is not divisible by 11. Therefore, 1195 is not divisible by 11.

Since 1195 is divisible by 5, 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 sequence, such as 1 to 100, in a grid format. 

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 complete the grid.

1195 is not present in a basic prime chart, indicating it is not a prime number, but rather 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 1195 as 5 × 239. 

Step 2: Both 5 and 239 are prime numbers.

Thus, the prime factorization of 1195 is 5 × 239.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. Example: 2, 3, 5.

• Composite numbers: Natural numbers greater than 1 that have more than two divisors. Example: 4, 6, 8.

• Factors: Numbers that divide another number exactly without leaving a remainder. Example: Factors of 6 are 1, 2, 3, and 6.

• Divisibility: A condition where one number can be divided by another without leaving a remainder. Example: 10 is divisible by 2 and 5.

• Prime factorization: The expression of a number as the product of its prime factors. Example: The prime factorization of 18 is 2 × 3 × 3.