Is 20 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 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 that is 1.

As 20 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 20 has more than two factors, it is not a prime number. Few methods used to distinguish between prime and composite numbers. Few methods are:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. 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 20 is prime or composite.

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

Step 2: Divide 20 by 2. It is divisible by 2, so 2 is a factor of 20.

Step 3: Divide 20 by 3. It is not divisible by 3, so 3 is not a factor of 20.

Step 4: You can simplify checking divisors up to 20 by finding the root value. We then need to only check divisors up to the root value.

√20=4.474 

Step 5: When we divide 20 by 2, 3, and 4, it is divisible by 2 and 4.

Since 20 has more than 2 divisors, 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. The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 20 is not present in the list of prime numbers, so it is a composite number.

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

Step 1: We can write 20 as 2 x 10.

Step 2: In 2  10, 10 is a composite number. Further, break the 10 into 2  x 5.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 20 is 2 x 2 x  5.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Twin primes: The pair of prime numbers whose difference is 2 are called twin prime numbers. For example, (11, 13) is a pair of twin primes because the difference of 13 and 11 is 2.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.