Is 121 a Prime Number?

No, 121 is not a prime number, because it is divisible by more than two numbers.
 

According to the definition of a prime number, a prime number should have only two factors which are 1 and itself. 121 does not meet the definition of a prime number, as it has more than two factors which are 1,11 and 121. So 121 is not a prime number. The following are the methods to be used to find whether 121 is a prime number or not. 

1. Counting Divisors Method                                                                                                         
2. Divisibility Test
3. Prime Number Chart     
4. Prime Factorization Method          

In this method, we will find out the number of divisors that can divide the given number evenly. Based on the count of divisors, we will categorize the number as either prime or composite.

If the count of divisors is 2 then the number is a prime number. 

If the count of divisors is more than 2 then the number is composite.

Step 1: 1 is a common factor for all integers.

Step 2: Start dividing 121 by 2 and it cannot be divided by 2. So 2 is not a factor of 121.

Step 3: Then divide 121 by 3 and it cannot be divided by 3. So 3 is not a factor of 121.

Step 4: Check for divisors up to the integer part of the square root of 121, which is 11. 

√121 = 11.

Step 5: As we can find, 121 is divisible by 11.

Hence, 121 is not a prime number, because 121 has more than 2 divisors.

A divisibility test is a method used to find out if a number can be divided by another number. To check whether a number can be divided by another number, we need to divide it by the numbers from 1 to the square root of that number.

 Here, 121 can be divisible by more than two numbers. Hence, 121 is not a prime number. 
 

Listing the prime numbers till 121: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113.

121 is not among the numbers in the prime number chart.

Therefore, 121 is a composite number.
 

Prime factorization is the method in which a number can be represented as a product of its prime factors. In this method, we break down the number into its prime factors, whose product will obtain the original number.

The prime factorization of 121 is 11  11, as 121 is the square of 11. 
 

• Prime numbers: Prime numbers are the numbers greater than 1 which are divisible by only 1 and itself. For example: 2,3,5…

• Factor: A number that can be multiplied with another number to obtain the required number. For example, 4 and 3 can be multiplied together to obtain 12. Hence, 4 and 3 can be considered as factors of 12.

• Composite numbers: The numbers which are greater than 1 and have more than two factors are called composite numbers. For example: 4,6,8,10,...

• Divisibility: The property of a number that can be evenly divisible by another number.For example, 12 can be divisible by 1,2,3,4,6 and 12