Is 3599 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 a 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.

To determine if 3599 is a prime number, we need to check its factors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 3599 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• Counting Divisors Method
  
   
• Divisibility Test
  
   
• Prime Number Chart
  
   
• 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 numbers as prime or composite.

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 3599 is prime or composite.

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

Step 2: Divide 3599 by 2. It is not divisible by 2.

Step 3: Divide 3599 by 3. It is not divisible by 3.

Step 4: You can simplify checking divisors by finding the square root value. We then need to only check divisors up to the square root value, which is approximately 60.

Step 5: When we divide 3599 by 11, we find that it is divisible. Therefore, 11 is a factor of 3599.

Since 3599 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 9, which is not even, so 3599 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 3599 is 26. Since 26 is not divisible by 3, 3599 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 3599 is not divisible by 5.

Divisibility by 7: Use the double and subtract method; 3599 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits of 3599 is 0, which is divisible by 11, so 3599 is divisible by 11. Since 3599 is divisible by 11, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write numbers in a range, for example, up to 100.

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 its multiples.

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

Step 5: Repeat this process until you reach the range. Through this process, you obtain a list of prime numbers.

Since 3599 is not in the list of prime numbers, it is a composite number.

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

Step 1: We can write 3599 as 11 × 327.

Step 2: In 11 × 327, 327 is a composite number. Further, break 327 into 3 × 109.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 3599 is 11 × 3 × 109.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
  
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 is a prime number.
  
   
• 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.
  
   
• Divisibility rules: Rules that help quickly determine whether one number is divisible by another without performing division.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.