Is 775 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 775 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 775 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 775 is prime or composite.

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

Step 2: Divide 775 by 5. It is divisible by 5, so 5 is a factor of 775.

Step 3: Divide 775 by 7. It is not divisible by 7, so 7 is not a factor of 775.

Step 4: You can simplify checking divisors up to 775 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 775 by 5, 25, and 31, it is divisible by 5 and 31.

Since 775 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 5. Five is an odd number, which means that 775 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 775 is 19. Since 19 is not divisible by 3, 775 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 5. Therefore, 775 is divisible by 5.

Divisibility by 7: The last digit in 775 is 5. To check divisibility by 7, double the last digit (5 × 2 = 10). Then, subtract it from the rest of the number (77 - 10 = 67). Since 67 is not divisible by 7, 775 is also not divisible by 7. 

Divisibility by 11: In 775, the difference between the sum of the digits in odd positions (7 + 5 = 12) and the sum of the digits in even positions (7) is 5. This would mean that 775 is not divisible by 11.

Since 775 is divisible only by 5 and other numbers, 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 the following steps.

Step 1: Write numbers from 1 to 1000 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 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 up to 1000.

The list does not include 775, so 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 775 as 5 × 155.

Step 2: In 5 × 155, 155 is a composite number. Further, break the 155 into 5 × 31.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 775 is 5 × 5 × 31.

• 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 factorization: The process of breaking down a number into its prime factors.
   
• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.