Is 325 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 325 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 325 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some of these methods are:

1. Counting Divisors Method
2. Divisibility Test Prime
3. Number Chart
4. 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 or 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 325 is prime or composite.

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

Step 2: Divide 325 by 5. It is divisible by 5, so 5 is a factor of 325.

Step 3: Check further divisors. Divide 325 by 13, and it is divisible, so 13 is also a factor.

Step 4: You can simplify checking divisors by finding the root value. We then need to only check divisors up to the root value. Since 325 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: 325 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 325 is 10. Since 10 is not divisible by 3, 325 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 325 is divisible by 5.

Divisibility by 7: Perform the divisibility test, and you will see 325 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is not divisible by 11, so 325 is not divisible by 11. Since 325 is divisible by 5 and 13, 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 these steps.

Step 1: Write 1 to 100 in 10 rows and 10 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 100. Since 325 is not on this list and can be further factored, 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 325 as 5 × 65.

Step 2: In 5 × 65, 65 is a composite number. Further, break the 65 into 5 × 13.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 325 is 5 × 5 × 13.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.

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

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

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

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