Is 649 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, such as: 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. As 649 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 649 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 numbers as prime or composite. 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 649 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Check divisibility by 2. Since 649 is odd, it is not divisible by 2. Step 3: Divide 649 by 3. The sum of the digits (6 + 4 + 9 = 19) is not divisible by 3, so it is not divisible by 3. Step 4: Divide 649 by 11. The alternating sum of the digits (6 - 4 + 9 = 11) is divisible by 11, so 11 is a factor of 649. Since 649 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 649 is odd, so it is not divisible by 2. Divisibility by 3: The sum of the digits in the number 649 is 19. Since 19 is not divisible by 3, 649 is also not divisible by 3. Divisibility by 5: The unit’s place digit is 9. Therefore, 649 is not divisible by 5. Divisibility by 7: Double the last digit (9 × 2 = 18), subtract it from the rest of the number (64 - 18 = 46). Since 46 is not divisible by 7, 649 is not divisible by 7. Divisibility by 11: The alternating sum of the digits (6 - 4 + 9 = 11) is divisible by 11, so 649 is divisible by 11. Since 649 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 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 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 table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 1000. The list includes numbers like 2, 3, 5, 7, 11, 13, etc. 649 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 649 as 11 × 59. Step 2: Both 11 and 59 are prime numbers. Step 3: The prime factorization of 649 is 11 × 59.

Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 649 is a composite number because it is divisible by 1, 11, 59, and 649. Divisibility rules: Rules that help determine whether one number is divisible by another without performing the actual division. Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 649 is 11 × 59. Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, and 5. Co-prime numbers: Two numbers that have only one common factor, which is 1, are co-prime numbers. For example, 11 and 59 are co-prime because their only common factor is 1.