import math

mod=998244353

def solve():
  a,b,c=map(int,input().split())
  g=math.gcd(a,c**140)
  a=g
  if (a**140)%c!=0:
    print(0)
    return
  a_tmp=1
  ans=b*200
  for i in range(1,140):
    if c==1:break
    a_tmp*=a
    while a_tmp%c==0:
      a_tmp//=c
    c_tmp=c
    g=-1
    while g!=1:
      g=math.gcd(a_tmp,c_tmp)
      c_tmp//=g
    if c_tmp>1:
      c_tmp=math.floor(math.pow(c_tmp,1/i)+0.0001)
      c_cnt=0
      while c%c_tmp==0:
        c//=c_tmp
        c_cnt+=1
      a_cnt=0
      a_tmp_tmp=a
      while a_tmp_tmp%c_tmp==0:
        a_tmp_tmp//=c_tmp
        a_cnt+=1
      #print(i,c_tmp)
      ans=min(ans,a_cnt*b//c_cnt)
  print(ans%mod)
t=int(input())
for _ in range(t):
  solve()