Is 902 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 902 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 902 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some of 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 is prime. -
• If the count is more than 2, then the number is composite.

Let’s check whether 902 is prime or composite.

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

Step 2: Divide 902 by 2. It is divisible by 2, so 2 is a factor of 902.

Step 3: Continue dividing 902 by other numbers such as 3, 5, 7, etc., until the square root of 902.

Since 902 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. This is called the Divisibility Test Method. -

Divisibility by 2: The number in the one's place is 2. Since 2 is an even number, 902 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 902 is 11. Since 11 is not divisible by 3, 902 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 2. Therefore, 902 is not divisible by 5. 

Divisibility by 7: Double the last digit (2 × 2 = 4) and subtract it from the rest of the number (90 - 4 = 86). Since 86 is not divisible by 7, 902 is not divisible by 7. -

Divisibility by 11: The difference between the sum of digits in odd positions (9 + 2) and even positions (0) is 11. Therefore, 902 is divisible by 11.

Since 902 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 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 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 have a table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

902 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 902 as 2 × 451.

Step 2: In 2 × 451, 451 is a composite number. Further, break 451 into 11 × 41.

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

Hence, the prime factorization of 902 is 2 × 11 × 41.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 902 is a composite number because it is divisible by 1, 2, 11, 41, 82, 451, and 902.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 902 is 2 × 11 × 41.

• Divisibility: A number is divisible by another if it divides the other number without leaving a remainder.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number because it is only divisible by 1 and 11.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.