Is 1431 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 1431 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 1431 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• 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 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 1431 is prime or composite.

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

Step 2: Divide 1431 by 2. It is not divisible by 2, so 2 is not a factor of 1431.

Step 3: Divide 1431 by 3. The sum of digits (1 + 4 + 3 + 1) is 9, which is divisible by 3, so 3 is a factor of 1431.

Step 4: You can simplify checking divisors up to 1431 by finding the square root value. We then need to only check divisors up to the root value. Since 1431 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 1. Since it is odd, 1431 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1431 is 9. Since 9 is divisible by 3, 1431 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 1431 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (1 × 2 = 2). Then, subtract it from the rest of the number (143 - 2 = 141). Since 141 is divisible by 7, 1431 is divisible by 7.

Divisibility by 11: In 1431, the sum of the digits in odd positions is 4, and the sum of the digits in even positions is 4. Since their difference is 0, which is divisible by 11, 1431 is divisible by 11. Since 1431 is divisible by 3, 7, and 11, 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. 1431 is not present in this list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1431 as 3 × 477.

Step 2: In 3 × 477, 477 is a composite number. Further, break the 477 into 3 × 159.

Step 3: Now break 159 into 3 × 53.

Step 4: Since 53 is a prime number, we have the prime factorization of 1431 as 3 × 3 × 3 × 53.

• Composite numbers: Natural numbers greater than 1 that have more than two factors. For example, 1431 is a composite number.
   
• Prime numbers: Natural numbers greater than 1 that have only two factors, 1 and the number itself. For example, 53 is a prime number.
   
• Divisibility rules: Set of rules to determine if one number is divisible by another without performing division.
   
• Prime factorization: Breaking down a number into its smallest prime factors. For example, 1431 can be factorized into 3 × 3 × 3 × 53.
   
• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 1431 include 1, 3, 9, 53, 159, 477, and 1431.