Is 638 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 638 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 638 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Here are a few methods:

• 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 numbers as prime or composite.

If there is a total count of only 2 divisors, then the number is prime.

If the count is more than 2, then the number is composite. Let’s check whether 638 is prime or composite.

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

Step 2: Divide 638 by 2. It is divisible by 2, so 2 is a factor of 638.

Step 3: Divide 638 by 3. It is not divisible by 3, so 3 is not a factor of 638.

Step 4: You can simplify checking divisors up to 638 by finding the root value. We then need to check divisors only up to the root value.

Step 5: When we divide 638 by 2, 11, and 29, it is divisible by 2, 11, and 29. Since 638 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 8. Since 8 is an even number, 638 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 638 is 17. Since 17 is not divisible by 3, 638 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 638 is not divisible by 5.

Divisibility by 7: The last digit in 638 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then subtract it from the rest of the number (63 - 16 = 47). Since 47 is not divisible by 7, 638 is not divisible by 7.

Divisibility by 11: In 638, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 6. The difference (9 - 6 = 3) is not divisible by 11, so 638 is not divisible by 11. Since 638 is divisible only by 2, 11, and 29, 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 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 from 1 to 1000. 638 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 multiplying those factors to obtain the original number.

Step 1: We can write 638 as 2 × 319.

Step 2: In 2 × 319, 319 is a composite number. Further, break down the 319 into 11 × 29.

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

Hence, the prime factorization of 638 is 2 × 11 × 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 it 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.

• Divisibility: A number is divisible by another if it can be divided without leaving a remainder.

• Factors: Numbers that divide a given 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.

• Prime factorization: The process of expressing a number as the product of its prime factors.