Is 697 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, such as:

• 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 697 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 697 has more than two factors, it is not a prime number.

A few methods are used to distinguish between prime and composite numbers.

Some 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 697 is prime or composite.

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

Step 2: Divide 697 by 2. It is not divisible by 2, so 2 is not a factor of 697.

Step 3: Divide 697 by 3. It is not divisible by 3, so 3 is not a factor of 697.

Step 4: Continue checking divisors up to the square root of 697, which is approximately 26.41.

Step 5: When we divide 697 by 17, it is divisible by 17 and gives a quotient of 41, which shows that 17 and 41 are factors of 697.

Since 697 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: 697 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 697 is 22. Since 22 is not divisible by 3, 697 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7, so 697 is not divisible by 5.

Divisibility by 7: Doubling the last digit (7 × 2 = 14) and subtracting from the rest (69 - 14 = 55) gives 55, which is divisible by 7. So, 697 is divisible by 7.

Divisibility by 11: The alternating sum is (6 - 9 + 7 = 4), which is not divisible by 11. Since 697 is divisible by 7, it has more than two factors and 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 the numbers 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 have marked all prime numbers up to 1000. Through this process, we will have a list of prime numbers.

697 is not present in the 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 697 as 17 × 41.

Step 2: Both 17 and 41 are prime numbers.

Hence, the prime factorization of 697 is 17 × 41.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 697 is a composite number because it is divisible by 1, 17, 41, and 697.

• Prime numbers: Numbers greater than 1 that have only two factors, 1 and themselves. For example, 17 is a prime number.

• Divisors: Numbers that divide another number completely without leaving a remainder. For example, the divisors of 6 are 1, 2, 3, and 6.

• Prime factorization: The expression of a number as the product of its prime factors. For example, 697 = 17 × 41.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.