Question

find the greatest prime number that is required to test as a divisor whether or not the following numbers are prime number is 109.​

Answer 1

Answer:

117/2 = 58 and the nearest prime numbers to 58 are 53 and 59.

So we know that no prime number bigger that 53 can possible be a factor.

Also - some simple testing (casting out the nines) shows us that 3 is a prime factor (always start with the smallest primes where possible) - and so we know we don’t even have to go for 53 - we just have to find the prime factors of 39 ( 59∗3=117 ).

Again just a quick inspection (ever digit is divisible by 3) shows us that 39 Must be divisible by 3 - so now the largest prime factor can be no larger than 13 - but 13 is a prime - so bingo.

We can see that 117=32∗13