Is 364 a Prime Number?

Numbers can be categorized as either prime numbers or composite numbers, based on the number of factors they have. 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 certain 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 364 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 364 has more than two factors, it is not a prime number. Various methods can be 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 counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. 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 is prime. If the count is more than 2, then the number is composite. Let’s check whether 364 is prime or composite.

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

Step 2: Divide 364 by 2. It is divisible by 2, so 2 is a factor of 364.

Step 3: Divide 364 by 3. It is not divisible by 3, so 3 is not a factor of 364.

Step 4: You can simplify checking divisors up to 364 by finding the square root value. We then need to check divisors up to this root value.

Step 5: When we divide 364 by 2, 4, 7, etc., it is divisible by several numbers.

Since 364 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 4. Four is an even number, which means that 364 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 364 is 13. Since 13 is not divisible by 3, 364 is not divisible by 3

Divisibility by 5: The unit’s place digit is 4. Therefore, 364 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (36 - 8 = 28). Since 28 is divisible by 7, 364 is divisible by 7.

Divisibility by 11: In 364, the sum of the digits in odd positions is 7, and the sum of the digits in even positions is 6. Since their difference is 1, which is not divisible by 11, 364 is not divisible by 11.

Since 364 is divisible by 2 and 7, among others, 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 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. 364 is not present in this list, 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 364 as 2 × 182.

Step 2: In 2 × 182, 182 is a composite number. Further, break the 182 into 2 × 91.

Step 3: Now break 91 into 7 × 13, which are prime numbers.

Step 4: Hence, the prime factorization of 364 is 2 × 2 × 7 × 13.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 364 is a composite number because it is divisible by several numbers.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 364 is 2 × 2 × 7 × 13.

• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 2 if it is even.

• Co-prime numbers: Two numbers that have no common factors other than 1. For example, 9 and 28 are co-prime.

• Perfect square: A number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is 4 squared.