Is 643 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers — depending on the number of factors they have.

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 have certain properties, such as:

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. The number 643 needs to be checked for these criteria to determine if it is prime.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 643 must be checked against this criterion, we will determine if it has any factors other than 1 and 643 itself. A few methods are used to distinguish between prime and composite numbers, including:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we categorize numbers accordingly:

If there is a total count of only 2 divisors, then the number is prime.

If the count is more than 2, then the number is composite. Let’s check whether 643 is prime or composite.

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

Step 2: Check divisibility by numbers less than the square root of 643, which is approximately 25.37.

Step 3: Test divisibility by all prime numbers less than 25 (i.e., 2, 3, 5, 7, 11, 13, 17, 19, 23).

Step 4: 643 is not divisible by any of these prime numbers. Since 643 has only two divisors, 1 and 643, it is a prime number.

The divisibility test method uses a set of rules to check whether a number is divisible by another number without leaving a remainder.

Divisibility by 2: 643 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits of 643 is 13, which is not divisible by 3.

Divisibility by 5: The last digit is 3, so 643 is not divisible by 5.

Divisibility by 7, 11, 13, 17, 19, and 23: Performing checks confirms that 643 is not divisible by any of these. Since 643 is not divisible by any numbers other than 1 and itself, it is a prime number.

A prime number chart can be created using “The Sieve of Eratosthenes” method. This involves:

Step 1: Write numbers from 1 to 1000 in rows and columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out all multiples of 2.

Step 4: Mark 3 as prime and cross out all multiples of 3.

Step 5: Continue this process with subsequent prime numbers until all numbers are either marked or crossed. 643 is not crossed out in this process, confirming it is a prime number.

Prime factorization involves breaking down a number into its prime factors.

If a number cannot be broken down further, it is prime.

For 643, testing divisibility by prime numbers less than the square root confirms that it cannot be factored further than 1 and 643 itself.

Thus, 643 is a prime number.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. Examples include 2, 3, 5, 7.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. Examples include 4, 6, 8, 9.

• Divisibility: The ability of one number to be divided by another without leaving a remainder.

• Co-prime numbers: Two numbers that have no common factors other than 1.

• Prime factorization: The process of expressing a number as a product of its prime factors.