Is 448 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 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 that is 1.

As 448 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 448 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

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 448 is prime or composite.

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

Step 2: Divide 448 by 2. It is divisible by 2, so 2 is a factor of 448.

Step 3: Divide 448 by 3. It is not divisible by 3, so 3 is not a factor of 448.

Step 4: You can simplify checking divisors up to 448 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 448 by 2, 4, 7, 8, and other numbers, it is divisible by several numbers. Since 448 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, which is even, meaning that 448 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 448 is 16. Since 16 is not divisible by 3, 448 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 448 is not divisible by 5.

Divisibility by 7: Using the rule for 7, 448 can be checked by doubling the last digit and subtracting it from the rest of the number, but manually dividing shows 448 is divisible by 7.

Divisibility by 11: In 448, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 4. Their difference is 4, which means that 448 is not divisible by 11. Since 448 is divisible by numbers like 2, 4, and 7, 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 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. 448 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 448 as 2 × 224.

Step 2: In 2 × 224, 224 is a composite number. Further, break the 224 into 2 × 112.

Step 3: Further break 112 into 2 × 56, and 56 into 2 × 28, and finally 28 into 2 × 14, and 14 into 2 × 7. Step 4: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 448 is 2 × 2 × 2 × 2 × 2 × 2 × 7.

• 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: A set of guidelines that help determine whether a number is divisible by another number without performing division.

• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 9 and 28 are co-prime.