Is 821 a prime number?

The number 821 has only 2 factors: 1 and 821. Since it cannot be divided by any other numbers without leaving a remainder, it is a prime number.

A number is considered prime if it has only two factors: 1 and the number itself. Since 821 has no other divisors, it qualifies as a prime number.

Given below are a few ways that can be used to find prime or composite numbers.

The different methods we can use to check if a number is a prime number are explained below:

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

For the counting divisors method, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 821 would simply be:

Divisors of 821 = 1, 821
Number of divisors = 2

Since 821 has only 2 divisors, it is a prime number.

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

In the divisibility method, a prime number has only 2 divisors: 1 and itself.

The divisors of 821 are 1 and 821.

Thus, 821 consists of only 2 factors and is a prime number.

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 800 - 1000 are:
809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.

Since 821 is listed in the chart, it is a prime number.

Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, and 5. Prime numbers are fundamental in number theory and cryptography.

Divisors: The numbers that divide evenly into another number. For example, the divisors of 821 are 1 and 821. A prime number has only two divisors: 1 and itself.

Counting Divisors Method: A method to determine if a number is prime by counting all of its divisors. If a number has exactly two divisors, it is a prime number. For example, 821 has only 1 and 821 as divisors.

Divisibility Test: A method to determine whether a number can be divided by another number without leaving a remainder. If no divisors are found other than 1 and the number itself, the number is prime.

Prime Factorization: Breaking down a number into the prime numbers that multiply to give that number. A prime number like 821 cannot be broken down into smaller prime factors because it is already prime.