Is 644 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 that is 1. As 644 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 644 has more than two factors, it is not 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 644 is prime or composite.

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

Step 2: Divide 644 by 2. It is divisible by 2, so 2 is a factor of 644.

Step 3: Divide 644 by 3. It is not divisible by 3, so 3 is not a factor of 644.

Step 4: Simplify checking divisors up to the square root of 644, which is approximately 25.

Step 5: Check divisibility by numbers up to 25. For instance, 644 is divisible by 4, 11, and 23. Since 644 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 value is 4. Since it is even, 644 is divisible by 2.

Divisibility by 3: The sum of the digits in 644 is 14. Since 14 is not divisible by 3, 644 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 4, and since it is not 0 or 5, 644 is not divisible by 5.

Divisibility by 7: 644 divided by 7 gives a remainder, so it is not divisible by 7. - Divisibility by 11: Alternate sum and difference of digits (6 - 4 + 4) = 6, which is not divisible by 11. Since 644 is divisible by 2 and other numbers, 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 sequence, such as 1 to 1000, in rows and columns.

Step 2: Leave 1 without marking, 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 have identified all primes up to 1000. By using this chart, you can see that 644 is not in the list of prime numbers, confirming it is composite.

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 644 as 2 × 322.

Step 2: Break down 322 into 2 × 161.

Step 3: 161 can be further divided by 7 and 23. Therefore, 644 = 2 × 2 × 7 × 23. Since the prime factorization of 644 includes more than two prime numbers, it is a composite number.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and itself, such as 3, 5, and 7.

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

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

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