Is 773 a prime number?

The number 773 has got only two factors that are capable of dividing the number completely without leaving any remainder. Thus, the number 773 is a prime number. The factors of 773 are 1 and 773.

A number is considered a prime number if it has only two distinct factors: 1 and itself. Since 773 only has these two factors, 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 773 would simply be:

Divisors of 773 = 1, 773
Number of divisors = 2

Since 773 only has two 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 only has 2 divisors, which are 1 and itself.

The divisors of 773 are 1 and 773.

Thus, 773 consists of only 2 factors, confirming it as a prime number.
 

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

The list of prime numbers under 1000 are:

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.

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

This method is only used for a non-prime number/composite number. Since 773 is a prime number, there is no prime factorization, as it only divides by 1 and itself.

Thus, the prime factorization for 773 does not exist in the traditional sense.
 

• Prime Number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, and 773.

• Divisor: A divisor is a number that divides another number without leaving a remainder. For example, the divisors of 773 are 1 and 773.

• Composite Number: A composite number is a positive integer greater than 1 that has more than two divisors. 773 is not a composite number because it only has two divisors, 1 and 773.

• Divisibility Rules: Divisibility rules are guidelines that help determine if a number is divisible by another number without performing the division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Prime Factorization: Prime factorization is the process of breaking down a number into its prime factors, which are the prime numbers that multiply together to give the original number. Since 773 is prime, it cannot be factorized further into prime numbers.