Is 1981 a prime number?

The number 1981 has 4 factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 1981 is a non-prime number. The factors of 1981 include 1, 7, 283, and 1981.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 1981 has more than 2 factors, hence making it a composite number.

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

The different methods we can use to check if a number is a prime number are explained below.

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

For the counting divisors method, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 1981 would simply be

Divisors of 1981= 1, 7, 283, 1981
Number of divisors= 4

The number 1981 can be considered composite.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

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

The divisors of 1981 are 1, 7, 283, and 1981.

 
Thus, 1981 consists of 6 factors that divide it completely without any remainder.
 

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 100 are;
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.

1981 is not present in the list, it is not a prime number.
 

This method is only used for a non-prime number/composite number. Since 1981 is a composite number, the prime factorization for 1981 is:

Factors of 1981 = 7 × 283
 

• Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers. A number like 1981, which has more than two divisors, is not prime.

• Divisors: Numbers that divide a given number exactly, leaving no remainder. For 1981, the divisors are 1, 7, 283, and 1981.

• Composite Number: A number that has more than two divisors. Since 1981 has six divisors, it is considered a composite number, not a prime number.

• Prime Factorization: The process of breaking down a composite number into its prime factors. For 1981, the prime factorization is 7 × 283.

• Divisibility Rule for 3: A rule used to determine if a number is divisible by 3. If the sum of a number's digits is divisible by 3, the number itself is divisible by 3. For example, the sum of the digits of 1981 (1 + 9 + 8 + 1 = 19) is not divisible by 3, so 1981 is not divisible by 3.