Is 650 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 650 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 650 has more than two factors, it is not a prime number. Several 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 650 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 650 by 2. It is divisible by 2, so 2 is a factor of 650. Step 3: Divide 650 by 3. It is not divisible by 3, so 3 is not a factor of 650. Step 4: You can simplify checking divisors up to 650 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 650 by 2, 5, 10, and 13, it is divisible by all these numbers. Since 650 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 0. Zero is an even number, which means that 650 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 650 is 11. Since 11 is not divisible by 3, 650 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 0. Therefore, 650 is divisible by 5. - Divisibility by 7: Double the last digit (0 × 2 = 0) and subtract it from the rest of the number (65 - 0 = 65). Since 65 is not divisible by 7, 650 is also not divisible by 7. - Divisibility by 11: Alternating sum of the digits (6 - 5 + 0 = 1) is not divisible by 11, so 650 is not divisible by 11. Since 650 is divisible by more than two numbers, 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 in sequences, typically up to a range like 1 to 100. Step 2: Leave 1 unmarked 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. 650 is not found within the range 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 650 as 2 × 325. Step 2: In 2 × 325, 325 is a composite number. Further, break down 325 into 5 × 65. Step 3: Break down 65 into 5 × 13. Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 650 is 2 × 5 × 5 × 13.

- 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: Numbers greater than 1 that have no divisors other than 1 and themselves. - Divisibility rules: Guidelines used to determine if one number is divisible by another without performing division. - Prime factorization: The process of expressing a number as the product of prime numbers. - Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to any given limit.