Is 453 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 453 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 453 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The method in which we count the number of divisors to categorize 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 453 is prime or composite.

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

Step 2: Divide 453 by 2. It is not divisible by 2, so 2 is not a factor of 453.

Step 3: Divide 453 by 3. It is divisible by 3, so 3 is a factor of 453.

Step 4: You can simplify checking divisors up to 453 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 453 by 3 and other numbers, it is divisible by 3.

Since 453 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place is 3. Since 3 is an odd number, 453 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 453 is 12. Since 12 is divisible by 3, 453 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 453 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (45 - 6 = 39). Since 39 is not divisible by 7, 453 is also not divisible by 7.

Divisibility by 11: In 453, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 5. The difference is 3, which means that 453 is not divisible by 11. Since 453 is divisible by 3, it has more than two factors.

Therefore, it 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 1 to 500 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 500. The list does not include 453, 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 453 as 3 × 151.

Step 2: In 3 × 151, both 3 and 151 are prime numbers.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 453 is 3 × 151.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 20 is a composite number because it is divisible by 1, 2, 4, 5, 10, and 20.

• Divisibility: A number is divisible by another if it can be divided without leaving a remainder. For example, 453 is divisible by 3.

• Prime factorization: The process of breaking down a number into its prime factors. For instance, the prime factorization of 453 is 3 × 151.

• Sieve of Eratosthenes: A method to find all prime numbers up to a certain number. It involves iteratively marking the multiples of each prime number starting from 2.

• Prime number: A natural number greater than 1 that is not divisible by any number other than 1 and itself. For example, 3 and 151 are prime numbers.