Is 671 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.

As 671 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 671 has more than two factors, it is not a prime number. Some 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 671 is prime or composite.

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

Step 2: Divide 671 by 2. It is not divisible by 2, so 2 is not a factor of 671.

Step 3: Divide 671 by 3. It is not divisible by 3, so 3 is not a factor of 671.

Step 4: Divide 671 by 11. It is divisible by 11, so 11 is a factor of 671.

Since 671 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 is odd, so 671 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 671 is 14. Since 14 is not divisible by 3, 671 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 671 is not divisible by 5.

Divisibility by 11: The alternating sum of the digits in 671 (6 - 7 + 1 = 0) is 0, which is divisible by 11. Therefore, 671 is divisible by 11.

Since 671 is divisible by 11, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write 1 to 1000 in charts.

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 numbers up to the square root of the maximum number in your range. Through this process, we will find that 671 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 671 as 11 × 61.

Step 2: Both 11 and 61 are prime numbers. Hence, the prime factorization of 671 is 11 × 61.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 671 is a composite number because it is divisible by 1, 11, 61, and 671.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 671 is 11 × 61.

• Divisibility rules: Guidelines to determine whether one number is divisible by another without performing division.

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

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