Is 461 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 461 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 461 has exactly two factors, it is a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods are:

• 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 461 is prime or composite.

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

Step 2: Divide 461 by 2. It is not divisible by 2, so 2 is not a factor of 461.

Step 3: Divide 461 by 3, 5, 7, etc., up to the approximate square root of 461.

Step 4: None of these numbers divides 461 evenly, confirming that 461 has no divisors other than 1 and itself. Since 461 has exactly 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: 461 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 461 is 11. Since 11 is not divisible by 3, 461 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 461 is not divisible by 5.

Divisibility by 7: There is no simple rule for 7, but dividing 461 by 7 gives a non-integer result, so 461 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits in 461 is 5. Since 5 is not divisible by 11, 461 is not divisible by 11. Since 461 is not divisible by any number other than 1 and itself, 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 numbers in a range, for example, 1 to 500.

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 largest number in your range. Through this process, we will have a list of prime numbers from 1 to 500. Since 461 is present in the list of prime numbers, it confirms that 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: Attempt to divide 461 by the smallest prime number, which is 2. It is not divisible.

Step 2: Continue checking with the next smallest primes like 3, 5, 7, etc.

Step 3: Since none of these primes divide 461 evenly, 461 itself is a prime number.

Thus, the prime factorization of 461 is just 461.

• Prime numbers: Natural numbers greater than 1 that have only two divisors: 1 and itself. For example, 5 is a prime number.

• Composite numbers: Natural numbers greater than 1 that have more than two divisors. For example, 12 is a composite number.

• Divisibility test: A set of rules to determine if one number is divisible by another without performing division.

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

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.