Is 1437 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 1437 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 1437 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 1437 is prime or composite.

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

Step 2: Divide 1437 by 2. It is not divisible by 2, so 2 is not a factor of 1437.

Step 3: Divide 1437 by 3. The sum of the digits, 1 + 4 + 3 + 7 = 15, which is divisible by 3, so 1437 is divisible by 3.

Step 4: Simplify checking divisors up to \(\sqrt{1437}\).

Step 5: When we check for divisors up to the square root, 1437 is divisible by 3 and 11. Since 1437 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 7, which is odd, meaning 1437 is not divisible by 2.

Divisibility by 3: The sum of the digits in 1437 is 15. Since 15 is divisible by 3, 1437 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1437 is not divisible by 5.

Divisibility by 7: Doubling the last digit (7 × 2 = 14) and subtracting it from the rest (143 - 14 = 129), which is divisible by 7, shows that 1437 is divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions (1 + 3 = 4) and even positions (4 + 7 = 11) is 7, which is divisible by 11. Therefore, 1437 is divisible by 11. Since 1437 is divisible by more than two distinct numbers, 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. 1437 is not present in the list of prime numbers because it is much larger than 100. Checking its factors, 1437 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 1437 as 3 × 479.

Step 2: Check 479 for further factorization.

Step 3: 479 is a composite number. Further break 479 into 11 × 43.

Step 4: Now we have the product consisting of only prime numbers. Hence, the prime factorization of 1437 is 3 × 11 × 43.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility rules: Guidelines to determine whether one number is divisible by another without performing division.
   
• Prime factorization: The process of breaking down a number into its prime factors.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to a given limit.