Is 467 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 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 467 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 467 has only 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 467 is prime or composite.

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

Step 2: Divide 467 by 2. It is not divisible by 2, so 2 is not a factor of 467.

Step 3: Divide 467 by 3. It is not divisible by 3, so 3 is not a factor of 467.

Step 4: You can simplify checking divisors up to 467 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 467 by any number other than 1 and 467, it is not divisible. Since 467 has only 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: The number in the ones' place value is 7. Seven is not an even number, which means that 467 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 467 is 17. Since 17 is not divisible by 3, 467 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 467 is not divisible by 5.

Divisibility by 7: The last digit in 467 is 7. To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (46 - 14 = 32). Since 32 is not divisible by 7, 467 is also not divisible by 7.

Divisibility by 11: In 467, the sum of the digits in odd positions is 11, and the sum of the digits in even positions is 6. This would mean that 467 is not divisible by 11. Since 467 is not divisible by any of these numbers, 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 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 includes 2, 3, 5, 7, 11, 13, 17, 19, 23, and continues. 467 is present in the list of prime numbers, so it is a prime 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 attempt to write 467 as a product of two numbers.

Step 2: Check divisibility by smaller prime numbers.

Step 3: Since 467 cannot be expressed as a product of smaller prime numbers, it is a prime number itself.

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

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.

• Divisibility rules: Rules that help determine whether one number is divisible by another without performing division.

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

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