Is 1414 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, which is 1.

As 1414 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 1414 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 1414 is prime or composite.

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

Step 2: Divide 1414 by 2. It is divisible by 2, so 2 is a factor of 1414.

Step 3: Divide 1414 by 3. It is not divisible by 3, so 3 is not a factor of 1414.

Step 4: You can simplify checking divisors up to 1414 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 1414 by 2, 707, and 353, it is divisible by 2, 707, and 353. Since 1414 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 4. Four is an even number, which means that 1414 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1414 is 10. Since 10 is not divisible by 3, 1414 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 1414 is not divisible by 5.

Divisibility by 7: Double the last digit (4 × 2 = 8). Subtract it from the rest of the number (141 - 8 = 133). Since 133 is not divisible by 7, 1414 is also not divisible by 7.

Divisibility by 11: The alternating sum of the digits is 1 - 4 + 1 - 4 = -6, which is not divisible by 11. Thus, 1414 is not divisible by 11. Since 1414 is divisible only by 2 and other factors, 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 with the next uncrossed number 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 the chosen range. Since 1414 is not in the list of prime numbers up to its square root, 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 write 1414 as 2 × 707.

Step 2: In 2 × 707, 707 is a composite number. Further, break the 707 into 7 × 101.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1414 is 2 × 7 × 101.

• 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 the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Divisibility: The ability of one number to be divided by another without leaving a remainder.

• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.