Is 704 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, which is 1.

As 704 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 704 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 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 704 is prime or composite.

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

Step 2: Divide 704 by 2. It is divisible by 2, so 2 is a factor of 704.

Step 3: Divide 704 by 3. It is not divisible by 3, so 3 is not a factor of 704.

Step 4: You can simplify checking divisors up to 704 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 704 by 2, 4, and 8, it is divisible by these numbers.

Since 704 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. It is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place value is 4. Four is an even number, which means that 704 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 704 is 11. Since 11 is not divisible by 3, 704 is also not divisible by 3.

Divisibility by 5: The unit's place digit is 4. Therefore, 704 is not divisible by 5.

Divisibility by 7: To check divisibility by 7 for 704, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (70 - 8 = 62). Since 62 is not divisible by 7, 704 is also not divisible by 7.

Divisibility by 11: In 704, the sum of the digits in odd positions is 7 + 4 = 11, and the sum of the digits in even positions is 0. The difference is 11, which is divisible by 11, so 704 is divisible by 11.

Since 704 is divisible by 2 and 11, it has more than two factors. Therefore, 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 numbers in a sequence, often 1 to 100, in rows and 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 have identified all prime numbers in the sequence. Through this process, we will have a list of prime numbers.

Since 704 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. Then multiply those factors to obtain the original number.

Step 1: We can write 704 as 2 × 352.

Step 2: In 2 × 352, 352 is a composite number. Further, break the 352 into 2 × 176.

Step 3: Continue factoring: 176 = 2 × 88, and 88 = 2 × 44, and 44 = 2 × 22, and 22 = 2 × 11.

Step 4: The prime factorization of 704 is 2 × 2 × 2 × 2 × 2 × 11.

• 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 that are only divisible by 1 and themselves, having exactly two distinct positive divisors.

• Divisibility Rules: A set of rules that help determine whether a number is divisible by another without performing full division.

• Prime Factorization: The process of expressing a number as the product of its prime factors.

• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.