Is 699 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 that is 1.

Since 699 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 699 has more than two factors, it is not a prime number. Several methods can be 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 is prime.
   
• If the count is more than 2, then the number is composite.

Let’s check whether 699 is prime or composite.

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

Step 2: Divide 699 by 2. It is not divisible by 2.

Step 3: Divide 699 by 3. It is divisible by 3, so 3 is a factor of 699.

Step 4: You can simplify checking divisors up to 699 by finding the square root value.

We then need to only check divisors up to the square root value.

Since 699 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 is 9, an odd number, so 699 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 699 is 24. Since 24 is divisible by 3, 699 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 699 is not divisible by 5.

Divisibility by 7: Doubling the last digit (9 × 2 = 18) and subtracting it from the rest of the number (69 - 18 = 51), we find 51 is divisible by 7, so 699 is divisible by 7.

Divisibility by 11: The sum of the digits in odd positions is 15, and the sum of the digits in even positions is 9. Their difference is 6, which is not divisible by 11.

Therefore, 699 is not divisible by 11. Since 699 is divisible by 3 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 these steps:

Step 1: Write numbers from 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 primes and crossed out non-primes.

Through this process, prime numbers are identified within the range.

Since 699 is not marked as a prime number, 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 699 as 3 × 233.

Step 2: In 3 × 233, 233 is a prime number.

Step 3: The prime factorization of 699 is 3 × 233.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.

• Divisibility: The property that a number can be divided by another number without leaving a remainder. For example, 15 is divisible by 3 because 15 divided by 3 equals 5.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Co-prime numbers: Two numbers with no common factors other than 1. For example, 8 and 15 are co-prime.

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