Solution: By Fermat's theorem as 24 and 7 are co­primes, remainder of 24^6 mod 7 =1. Hence,24^13 can be split up as 24^6* 24^6* 24 mod 7 = 1*1*3 mod 7 =3. Hence, remainder is 3. How is 24 mod 7 calculated here

can u plz elaborate how did they get 3 here as a remainder

24 mod 7 is 1. It is a direct result from Fermet's Theorem which says that if a and b are co-prime then a^E(b) mod b = 1.
E(b) is the euler no. of b. Here 24 and 7 are coprime and euler no. for 7 is 6 so 24^6 mod 7 = 1.