Is 667 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 667 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 667 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 667 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 667 by 2. It is not divisible by 2, so 2 is not a factor of 667. Step 3: Divide 667 by 3. It is not divisible by 3, so 3 is not a factor of 667. Step 4: Continue checking factors up to the square root of 667. Step 5: When we divide 667 by 23, it is divisible, so 23 is a factor of 667. Since 667 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 7. Since 7 is not even, 667 is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 667 is 19. Since 19 is not divisible by 3, 667 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 7. Therefore, 667 is not divisible by 5. - Divisibility by 7: Divide 667 by 7, and it is not divisible. - Divisibility by 11: Calculate the alternating sum of the digits (6 - 6 + 7 = 7). Since 7 is not divisible by 11, 667 is not divisible by 11. Since 667 is divisible by 23, 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 numbers in a sequence. 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 up to the desired range. Through this process, we identify prime numbers. Since 667 is not in the list of prime numbers up to 667, 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 667 as 23 × 29. Step 2: Both 23 and 29 are prime numbers, confirming that 667 is a composite number.

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. Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. Divisibility: A concept where one integer can be divided by another without leaving a remainder. Factorization: The process of decomposing a number into a product of other numbers, or factors. Co-prime numbers: Two numbers that have only 1 as their common factor.