Is 915 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 915 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 915 has more than two factors, it is not a prime number. Several 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 915 is prime or composite.

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

Step 2: Divide 915 by 2. It is not divisible by 2, so 2 is not a factor of 915.

Step 3: Divide 915 by 3. It is divisible by 3 (since the sum of the digits, 9 + 1 + 5 = 15, is divisible by 3), so 3 is a factor of 915.

Step 4: You can simplify checking divisors up to 915 by finding the square root value. We then need to only check divisors up to this value.

Step 5: When we divide 915 by 3 and 5, it is divisible by both.

Since 915 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, which is odd. Therefore, 915 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 915 is 15, which is divisible by 3. Thus, 915 is divisible by 3.

Divisibility by 5: The unit’s place digit is 5, which means that 915 is divisible by 5.

Divisibility by 7: Use the rule where you double the last digit and subtract it from the rest of the number (91 - 10 = 81). Since 81 is divisible by 7, 915 is also divisible by 7.

Divisibility by 11: In 915, the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 3, which is not divisible by 11. Therefore, 915 is not divisible by 11.

Since 915 is divisible by 3, 5, and 7, 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 from 1 to 1000 in rows.

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. 915 is not present in the list of prime numbers, 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 915 as 3 × 305.

Step 2: In 3 × 305, 305 is a composite number. Further, break 305 into 5 × 61.

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

Hence, the prime factorization of 915 is 3 × 5 × 61.

• 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 itself are called prime numbers. For example, 7 is a prime number.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to a specified integer.
   
• Divisibility rules: Rules that help determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7.