Is 346 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 346 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 346 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods include: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime 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 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 346 is prime or composite.

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

Step 2: Divide 346 by 2. It is divisible by 2, so 2 is a factor of 346.

Step 3: Divide 346 by 3. It is not divisible by 3, so 3 is not a factor of 346.

Step 4: You can simplify checking divisors up to 346 by finding the root value. We then need only to check divisors up to the root value.

Step 5: When we divide 346 by 2, it is divisible by 2.

Since 346 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 is 6. Six is an even number, which means that 346 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 346 is 13. Since 13 is not divisible by 3, 346 is also not divisible by 3. -

Divisibility by 5: The unit’s place digit is 6. Therefore, 346 is not divisible by 5. -

Divisibility by 7: The last digit in 346 is 6. To check divisibility by 7, double the last digit (6 × 2 = 12). Then, subtract it from the rest of the number (34 - 12 = 22). Since 22 is not divisible by 7, 346 is also not divisible by 7. -

Divisibility by 11: In 346, the sum of the digits in odd positions is 9 and the sum of the digits in even positions is 4. The difference is 5, which means that 346 is not divisible by 11.

Since 346 is divisible only by 2, 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 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.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 346 is not present in the list of prime numbers, so 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 346 as 2 × 173.

Step 2: In 2 × 173, 173 is a prime number.

Hence, the prime factorization of 346 is 2 × 173.

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

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 7 is a prime number. 

• Divisibility: The property that one number can be divided by another without leaving a remainder. 

• Prime factorization: Breaking down a composite number into a product of its prime factors. 

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