Is 395 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 395 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 395 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:

• 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 395 is prime or composite.

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

Step 2: Divide 395 by 2. It is not divisible by 2, so 2 is not a factor of 395.

Step 3: Divide 395 by 3. It is not divisible by 3, so 3 is not a factor of 395.

Step 4: You can simplify checking divisors up to 395 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 395 by 5, it is divisible by 5. Since 395 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place value is 5. Since 5 is not an even number, 395 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 395 is 17. Since 17 is not divisible by 3, 395 is also not divisible by 3.

Divisibility by 5: The unit's place digit is 5. Therefore, 395 is divisible by 5.

Divisibility by 7: The last digit in 395 is 5. To check divisibility by 7, double the last digit (5 × 2 = 10). Then, subtract it from the rest of the number (39 - 10 = 29). Since 29 is not divisible by 7, 395 is also not divisible by 7.

Divisibility by 11: In 395, the sum of the digits in odd positions is 12, and the sum of the digits in even positions is 9. The difference is 3, which means that 395 is not divisible by 11. Since 395 is divisible only by 5 and 79, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps.

Step 1: Write numbers from 1 to 400 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 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 400. Since 395 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. Then multiply those factors to obtain the original number.

Step 1: We can write 395 as 5 × 79.

Step 2: In 5 × 79, both 5 and 79 are prime numbers. Hence, the prime factorization of 395 is 5 × 79.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 395 is a composite number because 395 is divisible by 1, 5, 79, and 395.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 79 is a prime number.

• Factors: Numbers that divide another number exactly without leaving a remainder are called factors. For example, the factors of 10 are 1, 2, 5, and 10 because they divide 10 completely.

• Divisibility rules: Rules that help determine whether a number is divisible by another without performing division. For example, a number is divisible by 5 if its last digit is 0 or 5.

• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 395 is 5 × 79.