112 LearnersLast updated on May 26th, 2025
Is 817 a Prime Number?
The numbers that have only two factors which are 1 and itself are called prime numbers. For encryption, computer algorithms, barcode generation, prime numbers are used. In this topic, we will be discussing whether 817 is a prime number or not.
Is 817 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 817 has more than two factors, it is not a prime number.
Why is 817 Not a Prime Number?
The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 817 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
Using the Counting Divisors Method
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 817 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 817 by 2. It is not divisible by 2, so 2 is not a factor of 817. Step 3: Divide 817 by 3. It is not divisible by 3, so 3 is not a factor of 817. Step 4: You can simplify checking divisors up to 817 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 817 by 17, it is divisible by 17. Since 817 has more than 2 divisors, it is a composite number.
Using the Divisibility Test Method
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. Seven is an odd number, which means that 817 is not divisible by 2. Divisibility by 3: The sum of the digits in the number 817 is 16. Since 16 is not divisible by 3, 817 is also not divisible by 3. Divisibility by 5: The unit’s place digit is 7. Therefore, 817 is not divisible by 5. Divisibility by 11: The difference between the sum of the digits in odd positions (8 + 7 = 15) and even positions (1) is 14, which is not divisible by 11. Therefore, 817 is not divisible by 11. Since 817 is divisible by 17, it has more than two factors. Therefore, it is a composite number.
Using Prime Number Chart
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 1000 in 10 rows and 100 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 1000. 817 is not present in the list of prime numbers, so it is a composite number.
Using the Prime Factorization Method
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 817 as 17 × 48. Step 2: In 17 × 48, both 17 and 48 are composite numbers. Further, break the 48 into 2 × 24. Step 3: Now we get the product consisting of only prime numbers and a composite number. Hence, the prime factorization of 817 is 17 × 2 × 2 × 2 × 3.
Common Mistakes to Avoid When Determining if 817 is Not a Prime Number
Children might have some misconceptions about prime numbers when they are learning about them. Here are some mistakes that might be made by children.
Mistake 1
Assuming That All Odd Numbers Are Prime
Solution: Children have an assumption that all odd numbers are prime numbers. They should be taught that except for 2, most prime numbers are odd, but not all odd numbers are prime. For example, 21 is an odd number, but it has more than two factors, which makes it a composite number.
Mistake 2
Confusing 1 as a Prime Number
Children should know the definition of a prime number as having only two factors. But 1 has only one factor, which is itself. 1 is a unique number that is neither a prime nor a composite number.
Mistake 3
Depending Too Much on Memorization
Children rely on memorizing the prime numbers. But they might forget whether 29 or 39 is prime. To avoid these kinds of problems, children should have knowledge of divisibility rules rather than depending on memorization.
Mistake 4
Applying Divisibility Rules Incorrectly
When children divide a number by another number, they might make mistakes in calculation. For example, children might make mistakes while dividing 72 by 3. Teach them shortcuts, like if the sum of the digits of a number is divisible by 3, then the number is also divisible by 3.
Mistake 5
Assuming That Negative Numbers Are Prime
Children might think that negative numbers can also be prime numbers. For example, they might apply the divisibility rule of 2 for -48 to check whether it is prime or not. They need to know that prime numbers are positive numbers greater than 1.
FAQ on is 817 a Prime Number?
1.Is 817 a perfect square?
2.What is the sum of the divisors of 817?
3.What are the factors of 817?
4.What are the closest prime numbers to 817?
5.What is the prime factorization of 817?
Important Glossaries for "Is 817 a Prime Number"
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: The process of expressing a number as the product of its prime factors. Divisibility rules: Guidelines to quickly determine if one number is divisible by another without performing division. Counting divisors method: A method used to determine if a number is prime or composite by counting its divisors. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
