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.

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

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.

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.

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.

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.

• 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.