Is 703 a Prime Number?

There are two main types of numbers —

prime numbers and composite numbers — based 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 only 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 such as:

• Prime numbers are positive and 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 703 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 703 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers.

Some of these methods include:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The method in which we count the number of divisors to categorize numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as either 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 703 is prime or composite.

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

Step 2: Divide 703 by 2. It is not divisible by 2, so 2 is not a factor of 703.

Step 3: Divide 703 by 3. It is not divisible by 3, so 3 is not a factor of 703.

Step 4: You can simplify checking divisors up to 703 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 703 by 19, it is divisible by 19. Thus, 19 is a factor of 703.

Since 703 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is completely divisible by another number. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 3, which is odd, indicating that 703 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 703 is 10. Since 10 is not divisible by 3, 703 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 703 is not divisible by 5.

Divisibility by 7: Double the last digit (3 × 2 = 6), and subtract it from the rest of the number (70 - 6 = 64). Since 64 is not divisible by 7, 703 is also not divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd and even positions is 4 (7+3 - 0). Since 4 is not divisible by 11, 703 is not divisible by 11.

Since 703 is divisible by 19, 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 these 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.

703 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 703 as 19 × 37.

Step 2: In 19 × 37, both 19 and 37 are prime numbers.

Step 3: Hence, the prime factorization of 703 is 19 × 37.

• Composite numbers: Natural numbers greater than 1 that have more than two distinct positive divisors 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: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 is a prime number because it is divisible only by 1 and 7.

• Divisibility rules: A set of rules that help determine whether a number is divisible by another number without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Co-prime numbers: Two or more numbers that have no common factors other than 1. For example, 8 and 15 are co-prime because their only common factor is 1.