Is 1472 a Prime Number?

There are two main types of numbers: prime numbers and composite numbers, depending on the number of factors they have. 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 have a few properties: -

• 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 1472 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 1472 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. Some methods include: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 would be prime. 
• If the count is more than 2, then the number is composite.

Let’s check whether 1472 is prime or composite.

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

Step 2: Divide 1472 by 2. It is divisible by 2, so 2 is a factor of 1472.

Step 3: Divide 1472 by 3. It is not divisible by 3, so 3 is not a factor of 1472.

Step 4: You can simplify checking divisors up to 1472 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 1472 by 2, 4, and 8, it is divisible by 2, 4, and 8.

Since 1472 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. It is called the Divisibility Test Method. 

Divisibility by 2: The number in the ones' place value is 2. Since 2 is an even number, 1472 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1472 is 14. Since 14 is not divisible by 3, 1472 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 2. Therefore, 1472 is not divisible by 5. 

Divisibility by 7: The last digit in 1472 is 2. To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (147 - 4 = 143)

Since 143 is not divisible by 7, 1472 is also not divisible by 7. -

Divisibility by 11: In 1472, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 5. This means that 1472 is not divisible by 11.

Since 1472 is divisible by several numbers, 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 these 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 the table consists of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100. The list includes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Since 1472 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 1472 as 2 × 736.

Step 2: In 2 × 736, 736 is a composite number. Further, break 736 into 2 × 368.

Step 3: Continue breaking it down: 368 can be written as 2 × 184 and 184 can be written as 2 × 92.

Step 4: 92 can be broken down into 2 × 46 and 46 as 2 × 23.

Step 5: Now we have the prime factors: 2 × 2 × 2 × 2 × 2 × 2 × 23.

Hence, the prime factorization of 1472 is 2^6 × 23.

• 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 divisors other than 1 and themselves. 

• Divisors: Numbers that divide another number exactly without leaving a remainder. 

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

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division.