Is 948 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 948 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 948 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 948 is prime or composite.

Step 1: All numbers are divisible by 1 and themselves

Step 2: Divide 948 by 2. It is divisible by 2, so 2 is a factor of 948.

Step 3: Divide 948 by 3. It is divisible by 3, so 3 is a factor of 948.

Step 4: You can simplify checking divisors by finding the square root value. Then, check divisors up to the square root value.

Step 5: When we divide 948 by 2, 3, and other numbers up to its square root, it is divisible by several numbers.

Since 948 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 8. Since 8 is an even number, 948 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 948 is 21. Since 21 is divisible by 3, 948 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 948 is not divisible by 5.

Divisibility by 7: Using the rule for 7, we find 948 is divisible by 7.

Divisibility by 11: In 948, the difference between the sums of the digits in odd positions and even positions is 3, which is not divisible by 11.

Since 948 is divisible by multiple numbers, it has more than two factors. Therefore, 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 numbers from 1 to 1000 in rows and columns as needed.

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 have marked all primes and crossed out non-primes up to 1000. Through this process, you will have a list of prime numbers.

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

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 948 as 2 × 474.

Step 2: In 2 × 474, 474 is a composite number. Further, break 474 into 2 × 237.

Step 3: Then factor 237 into 3 × 79.

Step 4: Now we have the product consisting of only prime numbers.

Hence, the prime factorization of 948 is 2 × 2 × 3 × 79.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 is a prime number.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.