Is 2047 a Prime Number?

Numbers can be categorized as prime or composite based on their factors.

A prime number is a natural number that is divisible only by 1 and itself. For example, 11 is a prime number because it is divisible by only 1 and 11.

A composite number is a positive number that is divisible by more than two numbers. For instance, 12 is divisible by 1, 2, 3, 4, 6, and 12, making it a composite number.

Prime numbers have specific properties:

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, which is 1.

Since 2047 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 2047 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, such as:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of divisors:

If there is a total count of only 2 divisors, then the number is prime.

If the count is more than 2, the number is composite. Let’s check whether 2047 is prime or composite.

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

Step 2: Divide 2047 by 2. It is not divisible by 2, so 2 is not a factor of 2047.

Step 3: Divide 2047 by 3 and other small prime numbers until we reach a divisor or confirm its primality. Through this process, 2047 is found to be divisible by 23 and 89, as 2047 = 23 × 89. Since 2047 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not, known as the Divisibility Test Method.

Divisibility by 2: 2047 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 2047 (2 + 0 + 4 + 7 = 13) is not divisible by 3, so 2047 is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 2047 is not divisible by 5.

Divisibility by 11: Alternating sum of digits (2 - 0 + 4 - 7 = -1) is not divisible by 11, so 2047 is not divisible by 11. Since 2047 is divisible by 23 and 89, it has more than two factors, confirming it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method:

Step 1: Write numbers from 1 to 100 (or more) in rows and columns.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you have a list of prime numbers. 2047 is not found in the list of prime numbers up to its closest primes, confirming it is composite.

Prime factorization involves breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: Start with the smallest prime number and check divisibility.

Step 2: 2047 can be expressed as 23 × 89. Step 3: Both 23 and 89 are prime numbers. This factorization confirms 2047 is not a prime number.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 2047 is composite because it is divisible by 1, 23, 89, and 2047.

• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.

• Divisibility: The ability for one number to be divided by another without leaving a remainder.

• Factors: Numbers that divide another number exactly without leaving a remainder.

• Prime factorization: Writing a number as a product of its prime factors, such as 2047 = 23 × 89.