Question

Which one of the following is the largest 3 digit prime number?
(a) 999
(b) 997
(c) 991
(d) 993

Answer 1

Hint: Try to recall the definition of prime numbers and identify which of the given four numbers are prime. Once you find all the primes out of the four options, report the largest among the options which are prime, as we are asked the largest 3 digit prime.

Complete step-by-step answer:
Before moving to the solution, let us talk about the definitions of Prime numbers. The numbers which are divisible by 1 and the number itself, and have no other factors are called primes. For example 3, 4, etc.
If you see the option (a) and option (d), they are not primes as the sum of their digits is 27 and 21, respectively, which are divisible by 3, so the numbers 999 and 993 are also divisible by 3. According to the divisibility rule of 3, if the sum of the digits of a number is divisible by three the number is also divisible by 3.
Now 991 and 997 are primes. Out of the two options, 997 is the larger one, so it is the largest prime among the options.
Also, 997 to be the largest three-digit prime 999 and 998 must not be primes. 999 is divisible by 3, so not a prime and 998 can’t be because 998 is even number and even numbers are for sure divisible by 2, so 997 is the largest 3 digit prime.
Hence, the answer to the above question is an option (b).

Note: Remember that there is no method to check whether a given number is a prime other than checking its divisibility by all the numbers which are smaller than it, which is an impossible task to perform manually with some time constraint. So, generally, we eliminate options that are clearly not prime numbers using the divisibility rules of 2,3,5,7,11,13,17 and 19. Once you check with these numbers and you find no factors among this, you can hope that the number is possibly a prime.