Is 676 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 676 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 676 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 676 is prime or composite.

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

Step 2: Divide 676 by 2. It is divisible by 2, so 2 is a factor of 676.

Step 3: Divide 676 by 13. It is divisible by 13, so 13 is a factor of 676.

Step 4: You can simplify checking divisors up to 676 by finding the root value. We then need to only check divisors up to the root value.

Since 676 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. Six is an even number, which means that 676 is divisible by 2.

Divisibility by 13: The number 676 is divisible by 13 since 676 divided by 13 equals 52, which is a whole number. Since 676 is divisible by more than one number other than 1 and itself, 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 10 rows and 100 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 from 1 to 1000.

Since 676 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 676 as 2 × 338.

Step 2: In 2 × 338, 338 is a composite number. Further, break the 338 into 2 × 169.

Step 3: Now, break 169 into 13 × 13.

Hence, the prime factorization of 676 is 2 × 2 × 13 × 13.

• 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.

• Divisibility: A method used to check if a number can be divided by another number without leaving a remainder.

• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.

• Prime factorization: The process of expressing a number as the product of its prime factors.