Is 633 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, which is 1. As 633 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 633 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 633 is prime or composite.

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

Step 2: Divide 633 by 2. It is not divisible by 2, so 2 is not a factor of 633.

Step 3: Divide 633 by 3. It is divisible by 3, so 3 is a factor of 633.

Step 4: We can simplify checking divisors up to the square root value of 633. We then need to only check divisors up to this root value. Step 5: When we divide 633 by 3, 211, and others, it is divisible by more numbers than itself and 1. Since 633 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 is 3, which is odd. Therefore, 633 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 633 is 12. Since 12 is divisible by 3, 633 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 633 is not divisible by 5.

Divisibility by 7: The last digit in 633 is 3. To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (63 - 6 = 57). Since 57 is divisible by 7, 633 is divisible by 7.

Divisibility by 11: In 633, the sum of the digits in odd positions is 6, and the sum of the digits in even positions is 3. The difference is 3, which is not divisible by 11. Since 633 is divisible by numbers other than 1 and itself, it has more than two factors and is a composite 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 sequence.

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. Since 633 is not present in the list of prime numbers, 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 start by dividing 633 by 3, which gives us 3 × 211.

Step 2: Check the divisibility of 211, which is a prime number.

Hence, the prime factorization of 633 is 3 × 211.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 633 is a composite number because it is divisible by 1, 3, 211, and 633.

• Prime numbers: These are natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 3 and 211 are prime numbers.

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

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 633 is 3 × 211.

• Sieve of Eratosthenes: A method for identifying prime numbers up to a certain limit by iteratively marking the multiples of each prime number starting from 2.