Is 625 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 625 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 625 has more than two factors, it is not a prime number. Few 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 625 is prime or composite.

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

Step 2: Divide 625 by 5. It is divisible by 5, so 5 is a factor of 625.

Step 3: Divide 625 by other numbers up to the square root of 625, which is 25.

Step 4: When we divide 625 by 5, it is divisible multiple times (625 = 5 × 5 × 5 × 5).

Since 625 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: 625 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 625 is 13, which is not divisible by 3.

Divisibility by 5: The unit place digit is 5, so 625 is divisible by 5.

Divisibility by 7: 625 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits of 625 is 5, which is not divisible by 11.

Since 625 is divisible by 5 multiple times, 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 from 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.

Since 625 is not on this list, 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: Start with the smallest prime number, which is 5.

Step 2: Divide 625 by 5. We have 625 = 5 × 125.

Step 3: Divide 125 by 5. We have 125 = 5 × 25.

Step 4: Divide 25 by 5. We have 25 = 5 × 5.

Step 5: Now we have 625 = 5 × 5 × 5 × 5.

The prime factorization of 625 is 5 × 5 × 5 × 5.

• 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 factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
   
• Divisibility: A number is divisible by another if it can be divided evenly without leaving a remainder.
   
• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.
   
• Square root: A value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5.