import math

mod=998244353

def slv():
    A,B,C=map(int,input().split())

    ps=[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]

    # print(len(ps))

    def calc(p:int)->int:
        a,b,c=A,B,C
        ca,cc=0,0
        while a%p==0:
            a//=p
            ca+=1
        while c%p==0:
            c//=p
            cc+=1
        
        return (10**50 if cc==0 else (ca*b)//cc,a,c)
    
    ret=10**50

    for p in ps:
        t,A,C=calc(p)
        ret=min(ret,t)
    
    if C>1:
    
        tmp=0
        tmp2=1
        while A%C==0:
            tmp+=B
            A//=C
        while B>1:
            A=math.gcd(A,C)
            t=-1
            a=A
            for i in range(1,21):
                if a%C==0:
                    t=i
                    break
                a*=A
            if t==-1:break
            tmp2*=pow(A,B%t)
            while tmp2%C==0:
                tmp2//=C
                tmp+=1
            tmp+=B//t
            B//=t
            A=a//C
        tmp2*=A
        while tmp2%C==0:
            tmp2//=C
            tmp+=1
        
        ret=min(ret,tmp)

    print(ret%mod)

T=int(input())

while T:
    T-=1
    slv()