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Last updated on May 26th, 2025

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Is 926 a Prime Number?

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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers play a significant role in various fields such as cryptography, number theory, and computer science. In this topic, we will explore whether 926 is a prime number.

Is 926 a Prime Number? for Global Students
Professor Greenline from BrightChamps

Is 926 a Prime Number?

There are two main categories for numbers —

prime numbers and composite numbers, determined by the number of factors they have.

 

A prime number has exactly two distinct positive divisors: 1 and itself.

For example, 5 is a prime number because it is divisible only by 1 and 5.

 

A composite number has more than two divisors.

For instance, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

 

Key properties of prime numbers include:

 

  • Prime numbers are greater than 1.
     
  • The only even prime number is 2.
     
  • They have exactly two factors: 1 and the number itself.
     
  • Any two distinct prime numbers are co-prime, meaning they have no common factors other than 1.
     
  • Since 926 has more than two factors, it is not a prime number.

 

is 926 a prime number

Professor Greenline from BrightChamps

Why is 926 Not a Prime Number?

The defining feature of a prime number is that it has exactly two divisors: 1 and itself. Since 926 has more than two factors, it is not a prime number. To distinguish between prime and composite numbers, several methods can be used, such as:

 

  • Counting Divisors Method
     
  • Divisibility Tests
     
  • Prime Number Chart
     
  • Prime Factorization
Professor Greenline from BrightChamps

Using the Counting Divisors Method

The counting divisors method involves determining the number of divisors a number has to classify it as prime or composite.

 

  • If a number has exactly 2 divisors, it is prime.
     
  • If there are more than 2 divisors, the number is composite.

 

Let’s determine if 926 is prime or composite.

 

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

 

Step 2: Divide 926 by 2. It is divisible by 2, so 2 is a factor of 926.

 

Step 3: Check divisibility by other numbers up to the square root of 926.

 

Since 926 has more than 2 divisors, it is a composite number.

Professor Greenline from BrightChamps

Using the Divisibility Test Method

The divisibility test method involves applying specific rules to determine if a number is divisible by another without a remainder.

 

Divisibility by 2: The last digit of 926 is 6, an even number, so it is divisible by 2.

 

Divisibility by 3: The sum of the digits in 926 is 17, which is not divisible by 3, so 926 is not divisible by 3.

 

Divisibility by 5: The last digit is not 0 or 5, so 926 is not divisible by 5.

 

Divisibility by 7: Applying the divisibility rule for 7, 926 is not divisible by 7.

 

Since 926 is divisible by 2 among others, it has more than two factors, making it a composite number.

Professor Greenline from BrightChamps

Using Prime Number Chart

The prime number chart uses the "Sieve of Eratosthenes" method to identify prime numbers.

 

Step 1: Write numbers from 1 to 1000 in a grid.

 

Step 2: Leave 1 as it is neither prime nor composite.

 

Step 3: Mark 2 and eliminate its multiples.

 

Step 4: Mark 3 and eliminate its multiples.

 

Step 5: Continue marking primes and eliminating multiples. From this process, we find the prime numbers.

 

Since 926 is not marked as a prime number, it is composite.

Professor Greenline from BrightChamps

Using the Prime Factorization Method

Prime factorization involves breaking down a number into its prime factors.

 

Step 1: Start with the smallest prime, 2. 926 ÷ 2 = 463.

 

Step 2: Check if 463 can be broken down further.

 

Step 3: 463 is a prime number.

 

Thus, the prime factorization of 926 is 2 × 463.

Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Determining if 926 is Not a Prime Number

Misunderstandings about prime numbers can lead to errors. Here are some typical mistakes:

Mistake 1

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Assuming All Large Numbers Are Composite

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It's a common belief that larger numbers are composite. However, many large numbers are prime.

 

For example, 467 is a prime number despite its size.

Ray Thinking Deeply About Math Problems

FAQ on is 926 a Prime Number?

1.Is 926 a perfect square?

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2.What is the sum of the divisors of 926?

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3.What are the factors of 926?

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4.What are the closest prime numbers to 926?

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5.What is the prime factorization of 926?

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Professor Greenline from BrightChamps

Important Glossaries for "Is 926 a Prime Number"

  • Composite numbers: Numbers greater than 1 that have more than two factors. For example, 926 is composite because it is divisible by 1, 2, 463, and 926.

 

  • Prime numbers: Numbers greater than 1 with exactly two distinct positive divisors: 1 and themselves. For example, 463 is a prime number.
     
  • Factors: Numbers that divide another number exactly. For instance, the factors of 6 are 1, 2, 3, and 6.
     
  • Divisibility Test: A method to determine if one number is divisible by another without remainder.
     
  • Prime Factorization: Breaking down a number into its prime factors. For example, the prime factorization of 926 is 2 × 463.
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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

Fun Fact

: She loves to read number jokes and games.

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