Is 1254 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers, determined by the number of factors they have.

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 3 only.

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

Prime numbers have certain properties, such as:

- Prime numbers are 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 numbers because their only common factor is 1.

Since 1254 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1254 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including:

• 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 whether it is prime or composite. Based on the divisor count:

- If there are only 2 divisors, the number is prime.

- If there are more than 2 divisors, the number is composite.

Let’s check whether 1254 is prime or composite.

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

Step 2: Divide 1254 by 2. It is divisible by 2, so 2 is a factor of 1254.

Step 3: Divide 1254 by 3. It is divisible by 3, so 3 is a factor of 1254.

Step 4: To simplify, check divisors up to the square root of 1254.

Since 1254 has more than 2 divisors, it is a composite number.

The divisibility test method uses a set of rules to determine whether a number is divisible by another number completely.

- Divisibility by 2: The number 1254 ends with 4, an even number, so it is divisible by 2.

- Divisibility by 3: The sum of the digits in 1254 is 12 (1+2+5+4), which is divisible by 3, so 1254 is divisible by 3.

- Divisibility by 5: The unit’s place digit is not 0 or 5, so 1254 is not divisible by 5

- Divisibility by 11: Alternating sum of digits 1 - 2 + 5 - 4 = 0, which is divisible by 11, so 1254 is divisible by 11.

Since 1254 is divisible by more numbers than 1 and itself, it is a composite number.

The prime number chart is a tool for identifying prime numbers using a method called “The Sieve of Eratosthenes.” In this method:

Step 1: Write numbers from 1 to 1000 in rows and columns.

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

Step 3: Mark 2 as a prime number and cross out all multiples of 2.

Step 4: Mark 3 as a prime number and cross out all multiples of 3.

Step 5: Continue this process until all prime numbers are identified.

1254 is not on the list of prime numbers, confirming it is composite.

Prime factorization involves breaking down a number into its prime factors.

Step 1: Divide 1254 by 2: 1254 = 2 × 627.

Step 2: Divide 627 by 3: 627 = 3 × 209.

Step 3: Divide 209 by 11: 209 = 11 × 19.

Step 4: 19 is a prime number.

Thus, the prime factorization of 1254 is 2 × 3 × 11 × 19.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. Example: 12 is composite because it is divisible by 1, 2, 3, 4, 6, and 12.
  
   
• Divisibility rules: Rules to determine if one integer is divisible by another without performing division. Example: A number is divisible by 3 if the sum of its digits is divisible by 3.
  
   
• Prime factorization: Breaking down a number into its prime number components. Example: 30 = 2 × 3 × 5.
  
   
• Even numbers: Numbers divisible by 2. Example: 4, 8, 10.
  
   
• Co-prime numbers: Two numbers with no common factors other than 1. Example: 8 and 15 are co-prime.