Is 714 a Prime Number?

There are two types of numbers, mostly

• prime numbers
   
• 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 714 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 714 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. 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 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 714 is prime or composite.

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

Step 2: Divide 714 by 2. It is divisible by 2, so 2 is a factor of 714.

Step 3: Divide 714 by 3. It is divisible by 3, so 3 is also a factor of 714.

Step 4: To simplify checking divisors up to 714, find the square root value. We then need to check divisors up to the root value.

Step 5: When we divide 714 by 2, 3, and 7, it is divisible by these numbers. Since 714 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 4, which is even, meaning that 714 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 714 is 12. Since 12 is divisible by 3, 714 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4, which means 714 is not divisible by 5.

Divisibility by 7: Double the last digit (4 × 2 = 8) and subtract it from the rest of the number (71 - 8 = 63). Since 63 is divisible by 7, 714 is divisible by 7.

Divisibility by 11: Alternating sum of digits (7 - 1 + 4 = 10) is not divisible by 11, so 714 is not divisible by 11. Since 714 is divisible by 2, 3, and 7, 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 1 to 1000 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 marked and crossed all numbers up to 1000, except 1. Through this process, we will have a list of prime numbers from 1 to 1000. 714 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 multiplying those factors to obtain the original number.

Step 1: We can write 714 as 2 × 357.

Step 2: In 2 × 357, 357 is a composite number. Further, break 357 into 3 × 119.

Step 3: Continue breaking down 119 to its prime factors, 7 × 17.

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 714 is 2 × 3 × 7 × 17.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Twin primes: The pair of prime numbers whose difference is 2 are called twin prime numbers. For example, (11, 13) is a pair of twin primes because the difference between 13 and 11 is 2.
   
• 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.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime because they have no common factors other than 1.