Is 835 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 835 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 835 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, including: 

• 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 835 is prime or composite.

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

Step 2: Divide 835 by 5. It is divisible by 5, so 5 is a factor of 835.

Step 3: Divide 835 by 3. It is not divisible by 3, so 3 is not a factor of 835.

Step 4: You can simplify checking divisors up to 835 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 835 by 5 and 167, it is divisible by both.

Since 835 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. Since 5 is not an even number, 835 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 835 is 16. Since 16 is not divisible by 3, 835 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 5. Therefore, 835 is divisible by 5. 

Divisibility by 7: For 835, double the last digit (5 × 2 = 10) and subtract it from the rest of the number (83 - 10 = 73). Since 73 is not divisible by 7, 835 is not divisible by 7. 

Divisibility by 11: The alternating sum of the digits is 8 - 3 + 5 = 10. Since 10 is not divisible by 11, 835 is also not divisible by 11.

Since 835 is divisible by more than 2 numbers, 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 1 to 1000 in a grid format.

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 for subsequent numbers until the grid is filled with marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

835 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 835 as 5 × 167.

Step 2: Both 5 and 167 are prime numbers.

Step 3: Hence, the prime factorization of 835 is 5 × 167.

• Prime numbers: Natural numbers greater than 1 that have only two factors, 1 and itself. For example, 7 is a prime number.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 10 is a composite number because it is divisible by 1, 2, 5, and 10.

• Factors: The numbers that divide a number exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

• Divisibility: A number is divisible by another if dividing them leaves no remainder. For example, 15 is divisible by 5.

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