Is 1375 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 1375 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 1375 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 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 1375 is prime or composite.

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

Step 2: Divide 1375 by 2. It is not divisible by 2, so 2 is not a factor of 1375.

Step 3: Divide 1375 by 5. It is divisible by 5, so 5 is a factor of 1375.

Step 4: Divide 1375 by 11. It is not divisible by 11, so 11 is not a factor of 1375.

Step 5: You can simplify checking divisors up to 1375 by finding the root value. We then need to only check divisors up to the root value.

Since 1375 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: 1375 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1375 is 16. Since 16 is not divisible by 3, 1375 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 1375 is divisible by 5.

Divisibility by 7: The last digit in 1375 is 5. To check divisibility by 7, double the last digit (5 × 2 = 10). Then, subtract it from the rest of the number (137 - 10 = 127). Since 127 is not divisible by 7, 1375 is not divisible by 7.

Divisibility by 11: In 1375, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 10. The difference is 2, which is not divisible by 11. Therefore, 1375 is not divisible by 11.

Since 1375 is divisible by 5, 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 in a range, such as 1 to 1000.

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 with the next numbers, marking primes and crossing out their multiples. Through this process, we will have a list of prime numbers up to 1000.

Since 1375 is not present in the list of prime numbers, 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 1375 as 5 × 275.

Step 2: In 5 × 275, 275 is a composite number. Further, break 275 into 5 × 55.

Step 3: Further, break 55 into 5 × 11. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1375 is 5 × 5 × 5 × 11.

• 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 numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing division.
   
• Prime factorization: The process of breaking down a number into its prime factors.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.