Is 385 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 385 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 385 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

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 385 is prime or composite.

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

Step 2: Divide 385 by 2. It is not divisible by 2, so 2 is not a factor of 385.

Step 3: Divide 385 by 3. It is not divisible by 3, so 3 is not a factor of 385.

Step 4: Continue checking divisors up to the square root of 385.

Step 5: When we divide 385 by 5, it is divisible by 5 (385 ÷ 5 = 77), so 5 is a factor of 385.

Step 6: Divide 385 by 7. It is divisible by 7 (385 ÷ 7 = 55), so 7 is a factor of 385. Since 385 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 is 5, which is odd, so 385 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 385 is 16. Since 16 is not divisible by 3, 385 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 385 is divisible by 5.

Divisibility by 7: Divide 385 by 7, and it is divisible (385 ÷ 7 = 55). Therefore, 385 is divisible by 7. Since 385 is divisible by 5 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. 385 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 385 as 5 × 77.

Step 2: In 5 × 77, 77 is a composite number. Further, break the 77 into 7 × 11.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 385 is 5 × 7 × 11.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 385 is a composite number because it is divisible by 1, 5, 7, 11, 35, 55, 77, and 385.

• Prime numbers: Natural numbers greater than 1 that are divisible by only 1 and themselves. For example, 11 is a prime number because it is only divisible by 1 and 11.

• Factors: Numbers that divide another number exactly without leaving a remainder are called factors. For example, the factors of 385 are 1, 5, 7, 11, 35, 55, 77, and 385.

• Divisibility rules: Techniques used to determine if one number is divisible by another without performing the actual division. For instance, a number is divisible by 5 if its last digit is 0 or 5.

• Prime factorization: The process of expressing a number as the product of its prime factors, such as 385 = 5 × 7 × 11.