Needs an edge case such as solution(10, 2, 5).

This is amazingly simple, but I'm not sure I understand how it can work.

There should be a test with maximum numbers like solution(10000000,19,23,25,27,28,29).
Meanwhile, your solution can't even handle solution(0,19,23,25,27,28,29).

An O(n * len(factors)) solution: https://www.codewars.com/kata/reviews/5e2837f1bb3beb00011a0b1f/groups/5e28612383dbcd0001385f8d
Is is supposed to pass?

updated description

If performance is required, then the input range should be specified.

My prime-factorization based solution became faster at n = 10000

Averages of 250 testcases
Random numbers up to 10^1: Prime factors: 0.000 s, naive = 0.000 s
Random numbers up to 10^2: Prime factors: 0.001 s, naive = 0.001 s
Random numbers up to 10^3: Prime factors: 0.007 s, naive = 0.004 s
Random numbers up to 10^4: Prime factors: 0.044 s, naive = 0.044 s
Random numbers up to 10^5: Prime factors: 0.289 s, naive = 0.456 s
Random numbers up to 10^6: Prime factors: 3.563 s, naive = 5.182 s
Random numbers up to 10^7: Prime factors: 26.995 s, naive = 56.739 s

Your code fails for 143 = 13 * 11, or other numbers which have prime factors other than 2,3,5 and 7

Updated ✔️

Could you include the constraint that leading zeroes are not allowed to the description?