Is 1466 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 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 that is 1.
• As 1466 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 1466 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:

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 1466 is prime or composite.

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

Step 2: Divide 1466 by 2. It is divisible by 2, so 2 is a factor of 1466.

Step 3: Divide 1466 by 3. It is not divisible by 3, so 3 is not a factor of 1466.

Step 4: You can simplify checking divisors up to 1466 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Check other potential factors like 7, 11, etc., to see if 1466 is divisible.

Since 1466 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. Six is an even number, which means that 1466 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1466 is 17. Since 17 is not divisible by 3, 1466 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 6. Therefore, 1466 is not divisible by 5.

Divisibility by 7: Check the alternate method for checking divisibility by 7.

Divisibility by 11: In 1466, the alternating sum of the digits is 1 - 4 + 6 - 6 = -3. This is not divisible by 11, so 1466 is not divisible by 11.

Since 1466 is divisible by more than two numbers, 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 numbers in a sequence up to a determined limit.

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 list is complete.

Through this process, we can determine that 1466 is not a prime number, as it is not in the list of prime numbers.

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 1466 as 2 × 733.

Step 2: In 2 × 733, check if 733 is a prime number.

Step 3: Since 733 is not a prime number, further break it down into its prime factors.

The prime factorization of 1466 is 2 × 733.

• 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 factorization: Breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Divisibility: A number is divisible by another if the division results in a whole number without remainder.

• Factors: The numbers that divide the 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.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.