Is 1388 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 1388 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 1388 has more than two factors, it is not a prime number. A 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 1388 is prime or composite.

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

Step 2: Divide 1388 by 2. It is divisible by 2, so 2 is a factor of 1388.

Step 3: Divide 1388 by 3. It is not divisible by 3, so 3 is not a factor of 1388.

Step 4: You can simplify checking divisors up to 1388 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1388 by 2, 4, and 347, it is divisible by these numbers. Since 1388 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 8. This is an even number, which means that 1388 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1388 is 20. Since 20 is not divisible by 3, 1388 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 8, so 1388 is not divisible by 5.

Divisibility by 7: Double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (138 - 16 = 122). Since 122 is not divisible by 7, 1388 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits in 1388 is 1 - 3 + 8 - 8 = -2, which is not divisible by 11. Since 1388 is divisible only by 2, among small 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 numbers sequentially in rows and 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 for other numbers until you reach the number you are checking. Through this process, we will have a list of prime numbers. 1388 is not present in that list, 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 1388 as 2 × 694.

Step 2: 694 is a composite number. Further, break 694 into 2 × 347.

Step 3: 347 is a prime number. Hence, the prime factorization of 1388 is 2 × 2 × 347.

• 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 factorization: The process of expressing a number as a 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 that have only 1 as their common factor.
   
• Even numbers: Numbers that are divisible by 2. For example, 4, 6, and 8 are even numbers.