Is 1416 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 1416 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 1416 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 numbers as prime and 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 1416 is prime or composite.

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

Step 2: Divide 1416 by 2. It is divisible by 2, so 2 is a factor of 1416.

Step 3: You can simplify checking divisors up to 1416 by finding the square root value. We then need to only check divisors up to the square root value.

Step 4: When we divide 1416 by 2, 3, 4, and so on, it is divisible by several numbers. Since 1416 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. Since 6 is an even number, 1416 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1416 is 12. Since 12 is divisible by 3, 1416 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 6. Therefore, 1416 is not divisible by 5.

Divisibility by 7: Dividing 1416 by 7 yields an integer, so 1416 is divisible by 7.

Divisibility by 11: The alternating sum of the digits in 1416 is 0. Since 0 is divisible by 11, 1416 is divisible by 11. Since 1416 is divisible by multiple numbers beyond 1 and itself, 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 numbers in a range, such as 1 to 100, 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 within that range. Since 1416 is not on the list of prime numbers, it is a composite number.

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 start with dividing 1416 by 2 to get 708.

Step 2: Divide 708 by 2 to get 354.

Step 3: Continue dividing by 2 to get 177.

Step 4: Divide 177 by 3 to get 59, which is a prime number. Step 5: The prime factorization of 1416 is 2 × 2 × 2 × 3 × 59.

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

• Divisibility rules: A set of rules that help determine whether one number is divisible by another.

• Co-prime numbers: Two numbers that have no common factors other than 1.

• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.