Is 340 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 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 340 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 340 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: -

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 340 is prime or composite.

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

Step 2: Divide 340 by 2. It is divisible by 2, so 2 is a factor of 340.

Step 3: Divide 340 by 3. It is not divisible by 3, so 3 is not a factor of 340.

Step 4: You can simplify checking divisors up to 340 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 340 by 2, 4, 5, etc., it is divisible by several numbers.

Since 340 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 0. Zero is an even number, which means that 340 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 340 is 7. Since 7 is not divisible by 3, 340 is also not divisible by 3. -

Divisibility by 5: The unit’s place digit is 0. Therefore, 340 is divisible by 5. -

Divisibility by 7: The last digit in 340 is 0. To check divisibility by 7, double the last digit (0 × 2 = 0). Then, subtract it from the rest of the number (34 - 0 = 34). Since 34 is not divisible by 7, 340 is also not divisible by 7. -

Divisibility by 11: In 340, the sum of the digits in odd positions is 3, and the sum of the digits in even positions is 4. This would mean that 340 is not divisible by 11.

Since 340 is divisible by more than two numbers, 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. As 340 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 340 as 2 × 170.

Step 2: In 2 × 170, 170 is a composite number. Further, break the 170 into 2 × 85.

Step 3: Further, break down 85 into 5 × 17.

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 340 is 2 × 2 × 5 × 17.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 18 is a composite number because 18 is divisible by 1, 2, 3, 6, 9, and 18.

• Prime factors: The prime numbers that multiply together to give the original number. For example, the prime factors of 30 are 2, 3, and 5.

• Divisibility rules: Rules that help determine whether one number is divisible by another without performing division.

• Natural numbers: Positive integers starting from 1, like 1, 2, 3, and so on.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.