Is 648 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 648 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 648 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 the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as prime and composite.

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 648 is prime or composite.

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

Step 2: Divide 648 by 2. It is divisible by 2, so 2 is a factor of 648.

Step 3: Divide 648 by 3. It is divisible by 3, so 3 is a factor of 648.

Step 4: You can simplify checking divisors up to 648 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 648 by 2, 3, and other numbers, it is divisible by several numbers. Since 648 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 8. Since 8 is an even number, 648 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 648 is 18. Since 18 is divisible by 3, 648 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 648 is not divisible by 5.

Divisibility by 7: Check divisibility by 7 manually or using specific rules.

Divisibility by 11: Calculate the alternating sum of the digits in number 648. Since 648 is divisible by various numbers, 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 numbers in a range, such as 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 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 for other numbers. Through this process, we will have a list of prime numbers. Since 648 is not present in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 648 as 2 × 324.

Step 2: In 2 × 324, 324 is a composite number. Further, break the 324 into 2 × 162.

Step 3: Continue factorizing until only prime numbers remain.

Hence, the prime factorization of 648 is 2 × 2 × 2 × 3 × 3 × 3 × 3.

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

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing the division.

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

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

• Counting Divisors Method: A method used to determine if a number is prime or composite by counting its divisors.