Is 1150 a Prime Number?

Numbers can be categorized as prime or composite based on their factors.

A prime number is a natural number that is divisible only by 1 and itself.

For instance, 3 is a prime number because it has no divisors other than 1 and itself.

A composite number, on the other hand, has more than two divisors.

For example, 6 is a composite number because it is divisible by 1, 2, 3, and 6.

Some properties of prime numbers include: 

• Prime numbers are always greater than 1. 
   
• 2 is the only even prime number. 
   
• Prime numbers have exactly two factors: 1 and the number itself. 
   
• Any two distinct prime numbers are co-prime as their only common factor is 1.

Since 1150 has more than two factors, it is not a prime number.

A prime number is defined by having exactly two divisors: 1 and itself. Since 1150 has more than two factors, it is not a prime number. There are various methods to determine if a number is prime or composite, 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 if it is prime or composite.

If a number has exactly 2 divisors, it is prime.

 If it has more than 2, it is composite.

Let’s check whether 1150 is prime or composite:

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

Step 2: Divide 1150 by 2. It is divisible by 2, so 2 is a factor of 1150.

Step 3: Divide 1150 by 5. It is divisible by 5, so 5 is a factor of 1150.

Step 4: Other checks up to the square root of 1150 reveal that it is also divisible by 10, 23, 46, 50, and 115.

Since 1150 has more than 2 divisors, it is a composite number.

The divisibility test method uses rules to determine if a number is divisible by another without a remainder. 

Divisibility by 2: 1150 ends in 0, so it is divisible by 2.

Divisibility by 3: The sum of the digits (1+1+5+0 = 7) is not divisible by 3, so 1150 is not divisible by 3. 

Divisibility by 5: 1150 ends in 0, so it is divisible by 5. 

Divisibility by 7: Checking 1150 for divisibility by 7 reveals it is not divisible. 

Divisibility by 11: The difference between the sum of the digits in odd positions (1+5 = 6) and the sum of the digits in even positions (1+0 = 1) is 5, not divisible by 11.

1150 is divisible by 2, 5, and several other numbers, confirming it is composite.

A prime number chart, created using the Sieve of Eratosthenes, can be used to identify prime numbers.

Step 1: List numbers from 1 to 100 in a grid.

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

Step 3: Mark 2 as prime and cross out all its multiples.

Step 4: Mark 3 as prime and cross out all its multiples.

Step 5: Continue this process to identify primes up to 100.

1150 does not appear in a basic prime chart and is not a prime number for it has more factors.

Prime factorization involves expressing a number as a product of prime numbers:

Step 1: Begin by dividing 1150 by 2 to get 575.

Step 2: Divide 575 by 5 to get 115.

Step 3: Further divide 115 by 5 to get 23, which is a prime number.

The prime factorization of 1150 is 2 × 5 × 5 × 23.

• Composite numbers: Numbers greater than 1 with more than two factors. For example, 1150 is composite as it has factors beyond 1 and itself. 

• Prime numbers: Numbers greater than 1 with only two factors, 1 and the number itself. For example, 23 is prime. 

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

• Prime factorization: Expressing a number as a product of prime numbers. 

• Sieve of Eratosthenes: A method to find all prime numbers up to a specified integer.