def get(a: int, b: int, c: int, d: int) -> int:
    res = 0

    # a を d で割り切れるだけ割って、その回数を res に加える
    while a % d == 0:
        res += 1
        a //= d

    ta = 1
    for i in range(min(c, 150)):
        ta *= b
        if ta % d == 0:
            x = 0
            while ta % d == 0:
                x += 1
                ta //= d
            sub_c = c // (i + 1)
            sub_res = get(a * pow(b, c % (i + 1)), ta, sub_c, d)
            return x * sub_c + sub_res

    return res

from math import gcd

def check(a: int, b: int) -> int:
    g = gcd(a, b)
    while True:
        gg = gcd(a, g)
        if gg == 1:
            break
        a //= gg
    return a

def main():
    t = int(input())
    for _ in range(t):
        A, B, C = map(int, input().split())
        A //= check(A,C)
        print(get(1, A, B, C)%998244353)

if __name__ == "__main__":
    main()