import math

mod=998244353

def solve():
  a,b,c=map(int,input().split())
  a=math.gcd(a,c**140)
  ans=b*200
  i=0
  while i<140:
    i+=1
    if c==1:
      break
    a_tmp=a**i
    while a_tmp%c==0:
      a_tmp//=c
    #print(f"!{a_tmp}")
    c_tmp=c
    g=-1
    while g!=1:
      g=math.gcd(a_tmp,c_tmp)
      c_tmp//=g
    if c_tmp>1:
      if i==1:
        c_tmp=c_tmp
      else:
        c_tmp=math.floor(c_tmp**(1/i)+0.001)
      #print(f"?{c_tmp}")
      if c_tmp<=1:
        continue
      c_cnt=0
      while c%c_tmp==0:
        c//=c_tmp
        c_cnt+=1
      a_cnt=0
      while a%c_tmp==0:
        a//=c_tmp
        a_cnt+=1
      ans=min(ans,a_cnt*b//c_cnt)
      i=0
  print(ans%mod if c==1 else 0)
t=int(input())
for _ in range(t):
  solve()