vaivish1723 wrote:
If p, s, and t are positive prime numbers, what is the value of p^3s^3t^3?
(1) (p^3)*s*t=728
(2) t=13
Just to touch on some key points on this problem.
This problem is meant to test prime factorization.
So we need to break 728 into primes first.
This will give us (2^3) (13) (7) which is enough to solve the question.
Keep in mind some properties of primes and prime factorization
- All prime numbers except 2 and 5 end in '1','3','7' or '9'
- All prime numbers above 3 are of the form '6n+1' or '6n-1'
- The first prime number is 2 which is also the only even prime
- The Prime Numbers up to 100 are: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97)
- The square of any prime number greater than 3 is 1 more than a multiple of 12
- Verifying the primality of a given number 'n' can be done by trial division, that is to say dividing 'n' by all integer numbers smaller than √n
Hope this helps for future questions
Cheers!
J