Is 436 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 th at 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 436 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 436 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 436 is prime or composite.

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

Step 2: Divide 436 by 2. It is divisible by 2, so 2 is a factor of 436.

Step 3: Divide 436 by 3. It is not divisible by 3, so 3 is not a factor of 436.

Step 4: You can simplify checking divisors for 436 by finding the root value and only checking divisors up to the root value.

Step 5: When we divide 436 by 2, 4, and 109, it is divisible by all of them.

Since 436 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 6, which is an even number, meaning that 436 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 436 is 4 + 3 + 6 = 13. Since 13 is not divisible by 3, 436 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 6. Therefore, 436 is not divisible by 5. 

Divisibility by 7: The last digit in 436 is 6. To check divisibility by 7, double the last digit (6 × 2 = 12). Then, subtract it from the rest of the number (43 - 12 = 31). Since 31 is not divisible by 7, 436 is also not divisible by 7.

Divisibility by 11: Alternating sum and difference of the digits of 436 are 4 - 3 + 6 = 7. Since 7 is not divisible by 11, 436 is also not divisible by 11. Since 436 is divisible by 2 and 4, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created 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 a table consisting of marked and crossed boxes, except for 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 436 is not present in the list of prime numbers within this range, 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: We can write 436 as 2 × 218.

Step 2: In 2 × 218, 218 is a composite number. Further, break the 218 into 2 × 109.

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

Hence, the prime factorization of 436 is 2 × 2 × 109.

• 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 only two factors, 1 and themselves, are called prime numbers. 
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 6 are 1, 2, 3, and 6. 
   
• Divisibility rules: Guidelines that help determine if a number can be divided evenly by another number without performing the division. 
   
• Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7.