Is 692 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 692 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 692 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 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 692 is prime or composite.

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

Step 2: Divide 692 by 2. It is divisible by 2, so 2 is a factor of 692. -

Step 3: Divide 692 by 3. It is not divisible by 3, so 3 is not a factor of 692.

Step 4: You can simplify checking divisors up to 692 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 692 by 2, 4, and 173, it is divisible by 2, 4, and 173.

Since 692 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 2. Since 2 is an even number, 692 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 692 is 17. Since 17 is not divisible by 3, 692 is also not divisible by 3. -

Divisibility by 5: The unit’s place digit is 2. Therefore, 692 is not divisible by 5.

Divisibility by 7: The alternating sum of the digits of 692 is 5. Since 5 is not divisible by 7, 692 is also not divisible by 7.

Divisibility by 11: In 692, the alternating sum of the digits is 5. This means that 692 is not divisible by 11. Since 692 is divisible by 2 and 4, 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. The list includes 2, 3, 5, 7, 11, 13, 17, 19, etc.

692 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 692 as 2 × 346.

Step 2: In 2 × 346, 346 is a composite number. Further, break down 346 into 2 × 173.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 692 is 2 × 2 × 173.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 692 is a composite number because it is divisible by 1, 2, 4, 173, 346, and 692.

• Divisibility test: A method used to determine if one number is divisible by another without performing division.

• Prime factorization: The expression of a number as the product of its prime factors. For example, 692 is expressed as 2 × 2 × 173.

• Even numbers: Numbers that are divisible by 2 without leaving a remainder. For example, 692 is an even number.

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.