Is 1475 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers, depending on the number of factors they have. 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 only 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 have a few key properties: 

• Prime numbers are positive and always greater than 1. 
• 2 is the only even prime number. 
• They have exactly 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.
• Since 1475 has more than two factors, it is not a prime number.

A prime number has only two divisors: 1 and itself. Since 1475 has more than two factors, it is not a prime number. There are several methods to distinguish between prime and composite numbers, such as: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we classify numbers: -

• If there is a total of only 2 divisors, then the number is prime. 
• If the count is more than 2, then the number is composite.

Let’s check whether 1475 is prime or composite.

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

Step 2: Divide 1475 by 2. It is not divisible by 2, so 2 is not a factor of 1475.

Step 3: Divide 1475 by 3. It is not divisible by 3, so 3 is not a factor of 1475.

Step 4: Continue checking divisibility by other prime numbers up to the square root of 1475.

Since 1475 is divisible by numbers other than 1 and itself, such as 5, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely. This is called the Divisibility Test Method. -

Divisibility by 2: The number 1475 is odd, so it is not divisible by 2. -

Divisibility by 3: The sum of the digits in 1475 is 17, which is not divisible by 3. -

Divisibility by 5: The unit’s place digit is 5, so 1475 is divisible by 5. -

Divisibility by 7, 11, etc.: Check divisibility using appropriate rules.

Since 1475 is divisible by numbers other than 1 and itself, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers from 1 to a certain limit 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until the chart is complete with marked primes and crossed-out composites. Through this process, we have a list of prime numbers.

Since 1475 is not in the list of prime numbers, it is a composite number.

Prime factorization involves breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 1475 as 5 × 295.

Step 2: In 295, continue breaking it down into 5 × 59.

Step 3: Since 59 is a prime number, the prime factorization of 1475 is 5 × 5 × 59.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.

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

• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 5 if its last digit is 0 or 5.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, 5, 7, etc.

• Co-prime numbers: Two numbers that have no common divisors other than 1. For example, 8 and 15 are co-prime because their only common divisor is 1.