Is 1469 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 1469 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 1469 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:

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 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 1469 is prime or composite.

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

Step 2: 1469 is not divisible by 2 since it is odd.

Step 3: Divide 1469 by 3. The sum of its digits is 20, which is not divisible by 3, so 1469 is not divisible by 3.

Step 4: Divide 1469 by 7. 1469 divided by 7 is approximately 209.857, which is not a whole number.

Step 5: Continue checking divisors up to the approximate square root of 1469 (38.34). After testing possible divisors, it can be determined that 1469 is divisible by 37 and 39.

Since 1469 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: 1469 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1469 is 20. Since 20 is not divisible by 3, 1469 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 1469 is not divisible by 5.

Divisibility by 7: After performing calculations, 1469 is not divisible by 7.

Divisibility by 11: The alternating sum of digits is 2, which is not divisible by 11.

Since 1469 is divisible by numbers other than 1 and itself, it has more than two factors and 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 numbers in a sequence, such as 1 to 1500.

Step 2: Leave 1 without marking, 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 for all numbers up to the square root of the largest number in the list. Through this process, we will have a list of prime numbers.

1469 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 its prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1469 as 37 × 39.

Step 2: Check the factors 37 and 39. Here, 37 is a prime number, but 39 can be further factored into 3 × 13.

Step 3: The prime factorization of 1469 is 37 × 3 × 13.

• 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.

• Divisibility Test: A set of rules that help determine whether one number is divisible by another without performing division.

• Prime Factorization: The process of breaking down a number into its basic building blocks, which are prime numbers.

• Co-prime Numbers: Two numbers that have only 1 as their common factor.