Is 1417 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 1417 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 1417 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:

• 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 1417 is prime or composite.

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

Step 2: Divide 1417 by 2. It is not divisible by 2, so 2 is not a factor of 1417.

Step 3: Divide 1417 by 3. It is not divisible by 3, so 3 is not a factor of 1417.

Step 4: You can simplify checking divisors up to 1417 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Continue checking divisibility by other numbers up to the square root of 1417. Since 1417 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 7, which is odd, so 1417 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1417 is 13. Since 13 is not divisible by 3, 1417 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7, so 1417 is not divisible by 5.

Divisibility by 7: Use the rule to check divisibility by 7. Since it does not divide evenly, 1417 is not divisible by 7.

Divisibility by 11: Use the rule to check divisibility by 11. Since it does not divide evenly, 1417 is not divisible by 11. Since 1417 has multiple divisors other than 1 and itself, 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 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 you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100. Since 1417 is not within this range, further verification with larger numbers or another method is needed to confirm its compositeness. Checking with divisibility methods confirms 1417 is composite.

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 1417 as 1 × 1417.

Step 2: Check for divisibility by any smaller prime numbers.

Step 3: Through testing, find that 1417 can be broken down into 19 × 74, with 74 being 2 × 37.

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1417 is 19 × 2 × 37.

• 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.

• 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.

• Divisibility rules: Guidelines that help determine whether a number is divisible by another without performing full division.

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