primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009]
T = int(input())

def gcd(x, y):
  if y == 0:
      return x
  return gcd(y, x % y)

for i in range(T):
  n = int(input())
  p = 1
  q = 1
  res = 1
  i = 0
  while res * primes[i] <= n:
    # print(primes[i])
    res = res * primes[i]
    p = p * primes[i]
    q = q * (1 + primes[i])
    i = i + 1  
  g = gcd(p, q)
  p = p // g
  q = q // g
  print("{}/{}".format(p, q))