Question

The number of distinct primes dividing 13!+14!+15! Is?

Answer 1

The number of distinct primes that divide (13! +14! +15!) is equal to 6.

• 13!+14!+15! can be expressed as 13!(1+14+(14.15)), which can be further simplified to 13!.15².
• So, we can clearly see that the given expression will be divisible by all the primes till 13.
• A prime number is a number that is only divisible by itself and one.
• The total number of primes till 13 is equal to 6, i.e. 2,3,5,7,11,13.