Is 691 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. To determine if 691 is a prime number, we need to check its divisors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 691 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers: - 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 is prime. - If the count is more than 2, then the number is composite. Let’s check whether 691 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Divide 691 by 2, 3, 5, 7, and other numbers up to the square root of 691. Step 3: 691 is divisible by 13 (691 ÷ 13 = 53), indicating that it has more than two divisors. Since 691 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: 691 is odd, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in 691 is 16. Since 16 is not divisible by 3, 691 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 1. Therefore, 691 is not divisible by 5. - Divisibility by 7: Perform calculations to determine divisibility by 7, but 691 is not divisible by 7. - Divisibility by 13: 691 is divisible by 13, confirming it has more than two factors. Since 691 is divisible by 13, 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 multiples of 2. Step 4: Mark 3 because it is a prime number and cross out all multiples of 3. Step 5: Repeat this process until reaching the desired range. Through this process, we have a list of prime numbers. Since 691 is not on this list, 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 691 as 13 × 53. Step 2: Both 13 and 53 are prime numbers. Step 3: Hence, the prime factorization of 691 is 13 × 53.

1. Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 691 is a composite number because it is divisible by 1, 13, 53, and 691. 2. Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves are called prime numbers. For example, 13 is a prime number. 3. Divisibility: A number's ability to be divided by another number without leaving a remainder. For example, 12 is divisible by 3. 4. Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 691 is 13 × 53. 5. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.