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Last updated on April 28th, 2025

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Is 82 a Prime Number?

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Foundation
Intermediate
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The numbers that have only two factors, which are 1 and itself, are called prime numbers. For encryption, computer algorithms, and barcode generation, prime numbers are used. In this topic, we will be discussing whether 82 is a prime number or not.

Professor Greenline from BrightChamps

Is 82 a Prime Number?

There are two types of numbers, mostly —

 

  • Prime numbers
     
  • 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 82 has more than two factors, it is not a prime number.

is 82 a prime number

Professor Greenline from BrightChamps

Why is 82 Not a Prime Number?

The characteristic of a prime number is that it has only two divisors: 1 and itself.

 

Since 82 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
Professor Greenline from BrightChamps

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 82 is prime or composite.

 

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

 

Step 2: Divide 82 by 2. It is divisible by 2, so 2 is a factor of 82.

 

Step 3: Divide 82 by 3. It is not divisible by 3, so 3 is not a factor of 82.

 

Step 4: You can simplify checking divisors up to 82 by finding the root value. We then need to only check divisors up to the root value.

 

Step 5: When we divide 82 by 2 and 41, it is divisible by both. Since 82 has more than 2 divisors, it is a composite number.

Professor Greenline from BrightChamps

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 2. Two is an even number, which means that 82 is divisible by 2.

 

Divisibility by 3: The sum of the digits in the number 82 is 10. Since 10 is not divisible by 3, 82 is also not divisible by 3.

 

Divisibility by 5: The unit’s place digit is 2. Therefore, 82 is not divisible by 5.

 

Divisibility by 7: To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (8 - 4 = 4). Since 4 is not divisible by 7, 82 is also not divisible by 7.

 

Divisibility by 11: In 82, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 2. Their difference is 6, which means that 82 is not divisible by 11.

 

Since 82 is divisible by 2 and 41, it has more than two factors. Therefore, it is a composite number.

Professor Greenline from BrightChamps

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 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.

 

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

 

82 is not present in the list of prime numbers, so it is a composite number.

Professor Greenline from BrightChamps

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 82 as 2 × 41. Step 2: Both 2 and 41 are prime numbers.

 

Hence, the prime factorization of 82 is 2 × 41.

Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Determining if 82 is Not a Prime Number

Ray Thinking Deeply About Math Problems

FAQ on is 82 a Prime Number?

1.Is 82 a perfect square?

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2.What is the sum of the divisors of 82?

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3.What are the factors of 82?

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4.What are the closest prime numbers to 82?

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5.What is the prime factorization of 82?

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Professor Greenline from BrightChamps

Important Glossaries for "Is 82 a Prime Number"

  • Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 82 is a composite number because 82 is divisible by 1, 2, 41, and 82
     
  • Prime numbers: Natural numbers greater than 1 that are divisible only by 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: The capacity of one number to be divided by another without leaving a remainder.
     
  • Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
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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.

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Max, the Girl Character from BrightChamps

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: She loves to read number jokes and games.

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