Browse · MATH Print → jmc number theory intermediate Problem Let N be the product of all odd primes less than 24. What remainder does N leave when divided by 24? Solution — click to reveal The odd primes less than 24=16 are 3,5,7,11,13. Then 3⋅5⋅7⋅11⋅13=(3⋅11)⋅7⋅(5⋅13)=33⋅7⋅65≡1⋅7⋅1≡7(mod16). Final answer 7 ← Previous problem Next problem →