Is 196 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 196 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 196 has more than two factors, it is not a prime number. Several 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 196 is prime or composite.

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

Step 2: Divide 196 by 2. It is divisible by 2, so 2 is a factor of 196.

Step 3: Divide 196 by 3. It is not divisible by 3, so 3 is not a factor of 196.

Step 4: You can simplify checking divisors up to 196 by finding the square root. We then need to only check divisors up to the root value, which is 14.

Step 5: When we divide 196 by 2, 4, 7, 14, it is divisible by these numbers.

Since 196 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 6. Since 6 is an even number, 196 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 196 is 16. Since 16 is not divisible by 3, 196 is also not divisible by 3.

Divisibility by 4: The last two digits of 196 are 96, which is divisible by 4.

Divisibility by 5: The unit’s place digit is 6. Therefore, 196 is not divisible by 5.

Divisibility by 7: For 196, take the last digit (6), double it (12), and subtract from the rest of the number (19 - 12 = 7). Since 7 is divisible by 7, 196 is also divisible by 7.

Divisibility by 11: In 196, the difference between the sum of the alternate digits is 1, which is not divisible by 11.

Since 196 is divisible by 2, 4, and 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 1 to 100 in 10 rows and 10 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 complete the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 196 is not present in this list of prime numbers, so 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 196 as 2 × 98.

Step 2: In 2 × 98, 98 is a composite number. Further, break the 98 into 2 × 49.

Step 3: Break 49 into 7 × 7. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 196 is 2 × 2 × 7 × 7.

• 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 with no divisors other than 1 and themselves. For example, 5 is a prime number because it only has divisors 1 and 5.
   
• Divisibility: A concept that determines if one number can be evenly divided by another without leaving a remainder. For example, 24 is divisible by 3.
   
• Perfect square: A number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it is 4 × 4.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.