Is 1471 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 because they have only one common factor, which is 1.
• As 1471 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1471 has exactly two factors, it is a prime number. Several methods are used to distinguish between prime and composite numbers. A few methods are: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 numbers as prime or composite. -

• 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 1471 is prime or composite. 

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

Step 2: Check divisibility by each number less than the square root of 1471 (approximately 38.35). 

Step 3: 1471 is not divisible by any number other than 1 and 1471 itself.

Since 1471 has only 2 divisors, it is a prime 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. We will test divisibility for numbers less than the square root of 1471 (approximately 38.35).

Divisibility by 2: 1471 is not divisible by 2 as it is odd. - Divisibility by 3: The sum of the digits (1 + 4 + 7 + 1 = 13) is not divisible by 3. -

Divisibility by 5: The last digit is not 0 or 5, so 1471 is not divisible by 5. -

Divisibility by 7: After checking, 1471 is not divisible by 7. -

Divisibility by 11 and other numbers up to 37: 1471 is not divisible by any of these numbers.

Since 1471 is not divisible by any number other than 1 and 1471 itself, it is a prime number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” However, for numbers greater than 100, we typically use other methods or pre-existing lists to determine primality.

1471 is not within the simple 1 to 100 prime number chart, so we rely on other methods to determine its primality. By checking divisibility, as done in previous sections, it is confirmed that 1471 is a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Since 1471 cannot be divided by any prime number below its square root (approximately 38.35) except 1 and 1471 itself, it cannot be broken down further and is already in its prime form. Therefore, 1471 is a prime number.

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 3, 5, 7, 11, etc. 

• Composite Numbers: Natural numbers greater than 1 that have more than two divisors. - Factors: Numbers that divide another number exactly without leaving a remainder. 

• Divisibility Test: A set of rules to determine whether one number is divisible by another. 

• Prime Factorization: Expressing a number as the product of its prime factors.