Is 637 a Prime Number?

There are two types of numbers, primarily — 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. Since 637 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 637 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 637 is prime or composite.

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

Step 2: Divide 637 by 2. It is not divisible by 2, so 2 is not a factor of 637.

Step 3: Divide 637 by 3. The sum of the digits (6 + 3 + 7 = 16) is not divisible by 3, so 3 is not a factor of 637.

Step 4: Check divisibility by 5. 637 does not end in 0 or 5, so it is not divisible by 5.

Step 5: Continue checking divisors up to the approximate square root of 637. By checking divisibility and finding that 637 is divisible by 7 (637 ÷ 7 = 91), we see that 7 is a factor.

Therefore, 637 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: 637 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits of 637 is 16, which is not divisible by 3.

Divisibility by 5: The unit's place digit is 7, so 637 is not divisible by 5.

Divisibility by 7: Dividing 637 by 7 gives a quotient of 91 with no remainder, so 637 is divisible by 7.

Divisibility by 11: The alternating sum of the digits (6 - 3 + 7 = 10) is not divisible by 11. Since 637 is divisible by 7, it has more than two factors and is therefore 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 these 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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers. Since 637 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 637 as 7 × 91.

Step 2: In 91, further break down into 7 × 13.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 637 is 7 × 7 × 13.

• Prime Numbers: Natural numbers greater than 1 that have only two factors, 1 and itself, are called prime numbers. For example, 11 is a prime number because it is divisible only by 1 and 11.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Divisibility Rules: A set of rules used to determine if one number is divisible by another without performing division explicitly.

• Prime Factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Co-Prime Numbers: Two numbers are co-prime if they have only one common factor, which is 1. For example, 8 and 15 are co-prime.