Is 695 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 695 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 695 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 695 is prime or composite.

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

Step 2: Divide 695 by 5. It is divisible by 5, so 5 is a factor of 695.

Step 3: Divide 695 by 139. It is divisible by 139, making 139 another factor of 695.

Since 695 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: 695 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 695 is 20. Since 20 is not divisible by 3, 695 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 695 is divisible by 5.

Divisibility by 7: The last digit in 695 is 5. To check divisibility by 7, double the last digit (5 × 2 = 10). Then subtract it from the rest of the number (69 - 10 = 59). Since 59 is not divisible by 7, 695 is also not divisible by 7.

Divisibility by 11: Alternating sum of digits gives (6 - 9 + 5) = 2, which is not divisible by 11.

Since 695 is divisible by numbers other than 1 and itself, it has more than two factors, and 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 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 end up with only marked numbers that are prime. Through this process, we will have a list of prime numbers up to 1000.

695 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 multiply those factors to obtain the original number.

Step 1: We can write 695 as 5 × 139.

Step 2: Both 5 and 139 are prime numbers.

Hence, the prime factorization of 695 is 5 × 139.

• 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: A method of expressing a number as the product of its prime factors.

• Divisibility rules: A set of rules that help determine if one number is divisible by another without performing the division.

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.

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