Is 647 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 647 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 647 has exactly two factors, it is 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 647 is prime or composite.

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

Step 2: Divide 647 by numbers up to the square root of 647, approximately 25.45.

Step 3: 647 is not divisible by any prime numbers up to 25 (2, 3, 5, 7, 11, 13, 17, 19, 23).

Since 647 has exactly 2 divisors, it is a prime 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: 647 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 647 is 17, which is not divisible by 3.

Divisibility by 5: 647 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 7: Check divisibility by performing long division or applying a specific rule. 647 is not divisible by 7.

Divisibility by 11: Alternate sum and difference of digits do not result in a multiple of 11. Since 647 is not divisible by any numbers other than 1 and itself, it is a prime 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 range, such as 1 to 1000.

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 the number in question. Through this process, 647 is identified as a prime number, as it is not crossed out.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: Since 647 is not divisible by any primes up to its square root, it remains as a single factor: 647 itself. 

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. Example: 647.

• Composite numbers: Natural numbers greater than 1 that have more than 2 divisors. Example: 12.

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

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

• Prime factorization: Expressing a number as a product of its prime factors.