Is 669 a Prime Number?

Numbers are classified as either prime or composite based on their 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. In contrast, 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 have the following properties: - 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. Since 669 has more than two factors, it is not a prime number.

A prime number has only two divisors: 1 and itself. Since 669 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization

The counting divisors method involves determining the number of divisors a number has to categorize it as prime or composite. Here's how you can apply it to 669: - If a number has exactly 2 divisors, it is prime. - If the count is more than 2, the number is composite. Let's check whether 669 is prime or composite: Step 1: All numbers are divisible by 1 and itself. Step 2: Check divisibility of 669 by numbers starting from 2. Step 3: 669 is divisible by 3 (since the sum of its digits 6+6+9=21 is divisible by 3), so it has a factor of 3. Step 4: Since 669 has more than 2 divisors, it is a composite number.

Divisibility tests help determine whether a number is divisible by another number without leaving a remainder: - Divisibility by 2: 669 is odd, so not divisible by 2. - Divisibility by 3: The sum of the digits of 669 is 21, which is divisible by 3. Hence, 669 is divisible by 3. - Divisibility by 5: The last digit of 669 is 9, so it's not divisible by 5. - Divisibility by 7: Applying the divisibility rule for 7, 669 divided by 7 equals 95.57, which is not a whole number, so it is not divisible by 7. - Divisibility by 11: The alternating sum of digits is 3 (6-6+9), which is not divisible by 11. Since 669 is divisible by 3, it has more than two factors, making it a composite number.

A prime number chart is created using the "Sieve of Eratosthenes" method: Step 1: List numbers from 1 to 1000. Step 2: Leave 1 as it is neither prime nor composite. Step 3: Mark 2 as prime and cross out all multiples of 2. Step 4: Mark 3 as prime and cross out all multiples of 3. Step 5: Continue this process with the next unmarked number until all numbers are either marked or crossed. 669 is not marked as a prime number in this chart, confirming it is composite.

Prime factorization breaks down a number into its prime factors, which can then be multiplied to get the original number: Step 1: Start with the smallest prime number, 3, since 669 is not even. Step 2: Divide 669 by 3 to get 223, which is a prime number. Step 3: The prime factorization of 669 is 3 × 223.

- Composite numbers: Numbers greater than 1 that have more than two factors. - Divisibility rules: Guidelines to determine if a number is divisible by another without performing full division. - Prime factorization: Breaking down a number into its prime factors. - Sieve of Eratosthenes: A method to find all prime numbers up to a specific integer. - Co-prime numbers: Two numbers with only 1 as their common factor.