Is 117 a Prime Number?

No, 117 is not a prime number, because it is divisible by more than 2 numbers.
 

According to the definition of a prime number, a prime number should have only two factors which are 1 and itself. As 117 does not meet the definition of a prime number, it has more than two factors which are 1,3,9,13,39, and 117. So 117 is not a prime number. The following are the methods to be used to find whether 117 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: Note that, every number, including 117, is divisible by 1.

Step 2:Divide 117 by 2, as it is not divisible by 2. So 2 is not a factor of 117.

Step 3: Then divide 117 by 3 and it can be divided by 3. So 3 is a factor of 117.

Step 4: Likewise, we have to check up to the square root of 117.

√117=10.8167 = 11 (approximately)

Step 5: As we can find 117 is divided by 3 and 39.

Hence, 117 is not a prime number, because 117 has more than 2 divisors.

A divisibility test is a quick little trick used to find out if a number can be divided by another number. To check whether the 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, 117 is divisible by more than two numbers. Hence, 117 is not a prime number. 
 

Listing the prime numbers till 117: 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.

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

Therefore, 117 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 be equal to the original number.
The prime factorization of 117 is 3 х 3 х13.
    

• 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.