Is 725 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, 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. Since 725 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 725 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 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 725 is prime or composite.

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

Step 2: Divide 725 by 5. It is divisible by 5, so 5 is a factor of 725.

Step 3: Divide 725 by 7. It is not divisible by 7, so 7 is not a factor of 725.

Step 4: You can simplify checking divisors up to 725 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 725 by 5, it is divisible by 5. Since 725 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. It is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 5. Since 5 is an odd number, 725 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 725 is 14. Since 14 is not divisible by 3, 725 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 725 is divisible by 5.

Divisibility by 7, 11, etc.: Further divisibility tests show that 725 is not divisible by other small prime numbers. Since 725 is divisible by 5, 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.

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 for other primes until you reach the desired range. Through this process, we will have a list of prime numbers in a given range. Since 725 is not present 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 725 as 5 × 145.

Step 2: In 5 × 145, 145 is a composite number. Further, break the 145 into 5 × 29.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 725 is 5 × 5 × 29.

• 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.
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and itself are called prime numbers. For example, 7 is a prime number.
   
• Divisibility rules: A set of guidelines used to determine whether one number is divisible by another without performing division.
   
• Prime factorization: Writing a composite number as a product of its prime factors. For instance, 18 can be written as 2 × 3 × 3.
   
• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.