Is 1245 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 1245 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 1245 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 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 1245 is prime or composite.

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

Step 2: Divide 1245 by 2. It is not divisible by 2, so 2 is not a factor.

Step 3: Divide 1245 by 3. The sum of the digits (1+2+4+5=12) is divisible by 3, so 3 is a factor.

Step 4: You can simplify checking divisors up to the square root of 1245.

Since 1245 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 even, 1245 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1245 is 12. Since 12 is divisible by 3, 1245 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 1245 is divisible by 5.

Divisibility by 7: Use the rule for 7. 1245 divided by 7 is approximately 177.857, which is not a whole number, so it is not divisible by 7.

Divisibility by 11: Alternate sum rule gives (1-2)+(4-5) = -2, not divisible by 11. Since 1245 is divisible by 3 and 5, 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 the following steps:

Step 1: Write numbers in a range, say 1 to 1000.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

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

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

Step 5: Continue this process for other numbers. Through this process, we will have a list of prime numbers.

Since 1245 is not present in the list of prime numbers, 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 1245 as 3 × 415.

Step 2: Further break down 415 into 5 × 83.

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

Hence, the prime factorization of 1245 is 3 × 5 × 83.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1245 is a composite number because it is divisible by 1, 3, 5, 15, 83, 249, 415, and 1245.
  
   
• Prime Numbers: Numbers that have only two factors, 1 and themselves. For example, 83 is a prime number because it is divisible only by 1 and 83.
  
   
• Divisibility: A number is divisible by another if after dividing, the remainder is 0. For example, 1245 is divisible by 5 because 1245 divided by 5 leaves no remainder.
  
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 1245 include 1, 3, and 5.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes smaller than a given number.