Is 894 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 894 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 894 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods are: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 numbers as prime or composite. -

• 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 894 is prime or composite. -

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

Step 2: Divide 894 by 2. It is divisible by 2, so 2 is a factor of 894. 

Step 3: Divide 894 by 3. It is divisible by 3, so 3 is a factor of 894. 

Step 4: Continue checking divisors up to the square root of 894.

Since 894 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. This is called the Divisibility Test Method. -

Divisibility by 2: The number in the ones' place value is 4, an even number, which means that 894 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 894 is 21. Since 21 is divisible by 3, 894 is also divisible by 3. -

Divisibility by 5: The unit’s place digit is 4. Therefore, 894 is not divisible by 5. -

Divisibility by 7: To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (89 - 8 = 81). Since 81 is divisible by 7, 894 is divisible by 7. 

Divisibility by 11: In 894, the sum of the digits in odd positions is 12, and the sum of the digits in even positions is 9. Since 12 - 9 = 3 is not divisible by 11, 894 is not divisible by 11.

Since 894 is divisible by multiple 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 these 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 from 1 to 1000.

The list does not include 894, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and multiplying those factors to obtain the original number. -

Step 1: We can write 894 as 2 × 447. 

Step 2: In 2 × 447, 447 is a composite number. Further, break down 447 into 3 × 149.

The prime factorization of 894 is 2 × 3 × 149.

• 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: Numbers greater than 1 with no divisors other than 1 and itself. For example, 5 is a prime number. 

• Divisibility: The ability of one number to be divided by another without leaving a remainder. 

• Factors: Numbers that divide another number exactly without leaving a remainder. For example, factors of 4 are 1, 2, and 4. 

• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.