Is 350 a Prime Number?

There are two main types of numbers—prime numbers and composite numbers—based 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 have specific properties, such as: -

• 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.
• Since 350 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 350 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, such as: -

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 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 is prime. 
• If the count is more than 2, then the number is composite. Let’s check whether 350 is prime or composite:

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

Step 2: Divide 350 by 2. It is divisible by 2, so 2 is a factor of 350.

Step 3: Divide 350 by 3. It is not divisible by 3, so 3 is not a factor of 350.

Step 4: Check divisors up to the square root of 350 to simplify the process.

Step 5: When we divide 350 by 2, 5, and 7, it is divisible by 2, 5, and 7.

Since 350 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 ones' place value is 0. Zero is an even number, which means that 350 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 350 is 8. Since 8 is not divisible by 3, 350 is not divisible by 3. -

Divisibility by 5: The unit’s place digit is 0. Therefore, 350 is divisible by 5. 

Divisibility by 7: To check divisibility by 7, double the last digit (0 × 2 = 0) and subtract it from the rest of the number (35 - 0 = 35). Since 35 is divisible by 7, 350 is divisible by 7. 

Divisibility by 11: In 350, the sum of the digits in odd positions is 5, and the sum of the digits in even positions is 3. The difference is 2, which means that 350 is not divisible by 11.

Since 350 is divisible by 2, 5, and 7, 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 100 in 10 rows and 10 columns.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until the table is fully marked and crossed, except for 1. Through this process, we will have a list of prime numbers from 1 to 100.

The list includes 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. 350 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 350 as 2 × 175.

Step 2: In 2 × 175, 175 is a composite number. Further break down 175 into 5 × 35.

Step 3: Further break down 35 into 5 × 7.

Step 4: Now we get the product consisting only of prime numbers.

Hence, the prime factorization of 350 is 2 × 5 × 5 × 7.

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

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

• Divisibility rules: A set of rules that help determine whether a number is divisible by another without performing division.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1.

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