Is 630 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 630 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 630 has more than two factors, it is not a prime number. A 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 630 is prime or composite.

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

Step 2: Divide 630 by 2. It is divisible by 2, so 2 is a factor of 630.

Step 3: Divide 630 by 3. It is divisible by 3, so 3 is a factor of 630.

Step 4: You can simplify checking divisors up to 630 by finding the root value. We then need to only check divisors up to the root value. - Step 5: 630 is divisible by several numbers including 2, 3, 5, etc. Since 630 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: The number in the ones' place value is 0. Zero is an even number, which means that 630 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 630 is 9. Since 9 is divisible by 3, 630 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 0. Therefore, 630 is divisible by 5. - Divisibility by 7: By applying the rule for divisibility by 7, we find that 630 is divisible by 7.

Divisibility by 11: The alternating sum of digits (6 - 3 + 0 = 3) is not divisible by 11, so 630 is not divisible by 11. Since 630 is divisible by more than two numbers, 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 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. 630 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 630 as 2 × 315.

Step 2: 315 is a composite number. Further, break 315 into 3 × 105.

Step 3: Break 105 into 3 × 35. - Step 4: Break 35 into 5 × 7.

The prime factorization of 630 is 2 × 3 × 3 × 5 × 7.

• 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: Natural numbers greater than 1 that have no positive divisors other than 1 and itself.

• Factors: The numbers that divide a 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.

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

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.