Is 1172 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.

Since 1172 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 1172 has more than two factors, it is not a prime number.

Several methods are used to distinguish between prime and composite numbers.

A few methods are:

• 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 prime and composite numbers.

• If there is a total count of only 2 divisors, then the number would be prime.
   
• If the count is more than 2, then the number is composite.

Let’s check whether 1172 is prime or composite.

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

Step 2: Divide 1172 by 2. It is divisible by 2, so 2 is a factor of 1172.

Step 3: Checking further, 1172 is also divisible by other numbers like 4, 293, and 586.

Since 1172 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 one's place is 2, which is even. Therefore, 1172 is divisible by 2.

Divisibility by 3: The sum of the digits (1+1+7+2 = 11) is not divisible by 3, so 1172 is not divisible by 3.

Divisibility by 5: The unit's place digit is 2, so 1172 is not divisible by 5. 

Divisibility by 7, 11, etc., can be checked similarly.

Since 1172 is divisible by more than just 1 and itself, 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 1 to 100 in 10 rows and 10 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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1172 is not present in the list of prime numbers and is greater than 100, further testing confirms it is composite.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: Begin with the smallest prime, 2, which divides 1172 to give 586.

Step 2: 586 is also divisible by 2, giving 293, which is a prime number.

Thus, the prime factorization of 1172 is 2 × 2 × 293.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1172 is a composite number because it is divisible by 1, 2, 4, 293, 586, and 1172. 

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1172 is 2 × 2 × 293. 

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division. For example, a number is divisible by 2 if its last digit is even.

• Sieve of Eratosthenes: A method to find all prime numbers up to a certain limit by iteratively marking the multiples of each prime starting from 2. 

• Co-prime numbers: Two numbers that have no common factors other than 1. For example, 14 and 15 are co-prime.