Is 903 a Prime Number?

Numbers are primarily categorized into two types — prime numbers and composite numbers, based on the number of factors they possess. A prime number is a natural number that is divisible only by 1 and itself. For instance, 3 is a prime number because it is divisible by 1 and itself only.

Conversely, a composite number is a positive number that has more than two divisors. For example, 6 is divisible by 1, 2, 3, and 6, categorizing it as a composite number.

Prime numbers exhibit the following properties: -

• Prime numbers are positive integers greater than 1. 
• 2 is the only even prime number. 
• They have exactly two distinct factors: 1 and the number itself. 
• Any two distinct prime numbers are co-prime because they share only one common factor, which is 1.
• Since 903 has more than two factors, it is not a prime number.

A prime number is characterized by having only two divisors: 1 and itself. Since 903 has more than two factors, it is not a prime number. Several methods are used to differentiate between prime and composite numbers. Some of these methods include: -

• Counting Divisors Method 
• Divisibility Test 
• Prime Number Chart 
• Prime Factorization

The counting divisors method involves counting the number of divisors a number has to determine if it is prime or composite. Based on the count of the divisors:

• If there are exactly 2 divisors, the number is prime. 
• If the count exceeds 2, the number is composite.

Let’s examine whether 903 is prime or composite.

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

Step 2: Divide 903 by 2. It is not divisible by 2, so 2 is not a factor of 903.

Step 3: Divide 903 by 3. It is divisible by 3, so 3 is a factor of 903.

Step 4: You can simplify checking divisors up to 903 by finding the root value. We then need to check divisors only up to the square root value.

Step 5: When dividing 903 by 3, 9, and 13, it is divisible by 3 and 13.

Since 903 has more than 2 divisors, it is a composite number.

The divisibility test method uses a set of rules to determine whether a number can be completely divided by another number. -

Divisibility by 2: The last digit in 903 is 3, which is odd, so 903 is not divisible by 2. 

Divisibility by 3: The sum of the digits in 903 is 12 (9 + 0 + 3). Since 12 is divisible by 3, 903 is also divisible by 3. 

Divisibility by 5: The last digit is not 0 or 5, so 903 is not divisible by 5. 

Divisibility by 7: Doubling the last digit (3 × 2 = 6) and subtracting from the rest (90 - 6 = 84) shows 84 is divisible by 7. Therefore, 903 is divisible by 7. 

Divisibility by 11: The alternating sum of the digits (9 - 0 + 3 = 12) is not divisible by 11, so 903 is not divisible by 11.

Since 903 is divisible by multiple numbers besides 1 and itself, it is a composite number.

The prime number chart, created by the “Sieve of Eratosthenes” method, helps identify prime numbers.

Step 1: Write numbers from 1 to 1000.

Step 2: Leave 1 unmarked, as it is neither prime nor composite.

Step 3: Mark 2 and cross out all multiples of 2.

Step 4: Mark 3 and cross out all multiples of 3.

Step 5: Continue this process until all numbers are marked or crossed. Using this process, we identify prime numbers up to 1000.

Since 903 is not marked as prime, it is a composite number.

Prime factorization involves breaking down a number into its prime factors and multiplying them to reconstruct the original number.

Step 1: We can write 903 as 3 × 301.

Step 2: In 3 × 301, 301 is a composite number. Further, break 301 into 7 × 43.

Step 3: Now we have a product consisting only of prime numbers.

Hence, the prime factorization of 903 is 3 × 7 × 43.

• Composite numbers: Numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number as it is divisible by 1, 2, 3, 4, 6, and 12.

• Prime numbers: Numbers greater than 1 that have only two divisors, 1 and themselves. For example, 5 is a prime number.

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

• Divisibility rules: Guidelines to determine if a number can be divided completely by another number without a remainder.

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