Is 878 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 878 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 878 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: -

1. Counting Divisors Method
2. Divisibility Test 
3. Prime Number Chart 
4. Prime Factorization

The method in which we count the number of divisors to categorize 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 878 is prime or composite.

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

Step 2: Divide 878 by 2. It is divisible by 2, so 2 is a factor of 878.

Step 3: Divide 878 by 3. It is not divisible by 3, so 3 is not a factor of 878.

Step 4: You can simplify checking divisors up to 878 by finding the root value. We then need to check divisors only up to the root value.

Step 5: When we divide 878 by 2, 439, and other numbers, it is divisible by 2. Since 878 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, 878 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 878 is 23. Since 23 is not divisible by 3, 878 is also not divisible by 3. -

Divisibility by 5: The unit’s place digit is 8. Therefore, 878 is not divisible by 5. -

Divisibility by 7: The last digit in 878 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (87 - 16 = 71). Since 71 is not divisible by 7, 878 is also not divisible by 7. -

Divisibility by 11: In 878, the sum of the digits in odd positions is 15, and the sum of the digits in even positions is 8. The difference is 7, which is not divisible by 11.

Since 878 is divisible only by 2, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers from 1 to 1000 in rows and 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all 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 1000. The list does not include 878, 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 878 as 2 × 439. Step 2: In 2 × 439, 439 is a prime number.

Therefore, 878 consists of the prime factors 2 and 439.

• 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 a product of its prime factors.

• Divisibility: A measure of whether one number can be exactly divided by another without leaving a remainder.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers having only 1 as their common factor.