Is 392 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 392 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 392 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:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• 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 392 is prime or composite.

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

Step 2: Divide 392 by 2. It is divisible by 2, so 2 is a factor of 392.

Step 3: Divide 392 by 3. It is not divisible by 3, so 3 is not a factor of 392.

Step 4: You can simplify checking divisors up to 392 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 392 by 2, 4, 7, 14, 28, 56, 98, and 196, it is divisible by these numbers. Since 392 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 2. Since 2 is an even number, 392 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 392 is 14. Since 14 is not divisible by 3, 392 is also not divisible by 3.

Divisibility by 4: The last two digits in 392 are 92, which is divisible by 4. Therefore, 392 is divisible by 4.

Divisibility by 5: The unit’s place digit is 2. Therefore, 392 is not divisible by 5.

Divisibility by 7: When 392 is divided by 7, it results in a whole number (56). Thus, 392 is divisible by 7. Since 392 is divisible by more than two numbers, 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. 392 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 392 as 2 × 196.

Step 2: In 2 × 196, 196 is a composite number. Further, break the 196 into 2 × 98.

Step 3: Continue breaking down 98 into 2 × 49.

Step 4: Finally, break down 49 into 7 × 7.

Step 5: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 392 is 2 × 2 × 2 × 7 × 7.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 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 numbers: Natural numbers greater than 1 that have no positive divisors other than 1 and itself. For example, 11 is a prime number.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Prime factorization: A method of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.