Is 105 a Prime Number?

A prime number should not have factors more than 2 but 105 has 4 divisors. No, 105 is a composite number. 

The divisors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.  Therefore, 105 is a composite number. Composite numbers are the numbers which have factors more than 2.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. 105 has factors more than 2, so it is a composite number.

Given below are a few ways that can be used to find prime or composite numbers.

In this method, the divisors of a number are listed, and the number is checked, to be called a prime number. The counting divisors method for 105 would simply be

Divisors of 105 = 1, 3, 5, 7, 15, 21, 35, 105

Number of divisors = 8

The number 105 can be considered composite.
 

In divisibility method, the prime number only has 2 divisors, which are 1 and itself.

Divisors of 105 = 1, 3, 5, 7, 15, 21, 35, 105

As 105 has factors more than 2 then it is not a prime number
 

We write the prime number chart up to 10, which helps in sorting numbers.

The prime numbers from 100 to 200 are 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199. 105 is not on the list, so it is not a prime number.
 

This method is only used for a composite number. Since 105 is a composite number, prime factorization for 105 is: 3¹ x 5¹ x 7¹

Hence, the prime factors of 105 are 3, 5, and 7.

• Divisibility: The property of a number which can divide another number completely without leaving any remainder.

• Chart of Prime Numbers: The numbers which has only two factors are listed together.

• Composite Number: A number that has more than two positive divisors which are opposite to prime numbers which has only two factors.