Is 797 a prime number?

The number 797 has only two factors, 1 and 797, which means it cannot be divided by any other number without leaving a remainder. Hence, 797 is a prime number.

A number is considered a prime number if it only has two factors: 1 and itself. Since 797 can only be divided by 1 and 797 without any remainder, 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, we check whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 797 would simply be:

Divisors of 797 = 1, 797
Number of divisors = 2

Since 797 has only 2 divisors, it is a prime number.
 

In the divisibility test, we try dividing the number by prime numbers. If we cannot divide it evenly, the number is considered prime.

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

The divisors of 797 are 1 and 797.

Thus, 797 has only two factors, confirming it is a prime number.
 

The prime number chart is a list of prime numbers starting from 2 and going up to infinity.

The list of prime numbers from 700 to 1000 includes:

701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 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.

797 is present in the list, confirming it is a prime number.
 

This method is only used for non-prime (composite) numbers. Since 797 is a prime number, it does not have any prime factors other than itself.

Thus, the prime factorization of 797 is simply:

Factors of 797 = 797
 

• Prime Number: A natural number greater than 1 that has only two distinct divisors: 1 and itself. Example: 797, as it is divisible only by 1 and 797.

• Divisibility Test: A method used to determine if a number is divisible by another without leaving a remainder. If a number can only be divided by 1 and itself, it is a prime number.

• Counting Divisors Method: A technique used to find all the divisors of a number. If a number has exactly two divisors (1 and the number itself), it is prime. Example: 797 has divisors 1 and 797.

• Prime Factorization: The process of breaking down a composite number into its prime factors. Since 797 is prime, its prime factorization is simply 797.

• Composite Number: A natural number greater than 1 that has more than two divisors. Unlike prime numbers, composite numbers can be divided by numbers other than 1 and itself. Since 797 cannot be divided by any other number, it is not composite.