Is 708 a Prime Number?

There are two types of numbers, primarily —

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 natural 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, such as:

• 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.

As 708 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 708 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers.

A few methods are:

• 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 is prime. - If the count is more than 2, then the number is composite.

Let's check whether 708 is prime or composite.

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

Step 2: Divide 708 by 2. It is divisible by 2, so 2 is a factor of 708.

Step 3: Divide 708 by 3. It is divisible by 3, so 3 is a factor of 708.

Step 4: You can simplify checking divisors up to the square root of 708. We then need to only check divisors up to the root value.

Since 708 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 8. Since 8 is an even number, 708 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 708 is 15. Since 15 is divisible by 3, 708 is divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 708 is not divisible by 5.

Divisibility by 7: Double the last digit (8 × 2 = 16). Subtract it from the rest of the number (70 - 16 = 54). Since 54 is divisible by 7, 708 is divisible by 7.

Since 708 is divisible by more than two numbers, 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 1000 in a grid.

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: Continue this process until you reach the end of the table. Through this process, we will have a list of prime numbers up to 1000.

708 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 708 as 2 × 354.

Step 2: Break down 354 into 2 × 177.

Step 3: Break down 177 into 3 × 59.

Step 4: 59 is a prime number.

Thus, the prime factorization of 708 is 2 × 2 × 3 × 59.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 16 is a composite number because 16 is divisible by 1, 2, 4, 8, and 16.

• Prime numbers: Natural numbers greater than 1 that are divisible by only 2 numbers, which are 1 and itself. For example, 7 is a prime number.

• Divisibility rules: A set of rules that allow quick determination of whether one number is divisible by another.

• Prime factorization: The process of breaking down a number into its basic prime number components.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 15 are co-prime numbers.