```
def largestDivisibleSubset(self, nums):
"""
:type nums: List[int]
:rtype: List[int]
"""
# divisibility is transitive, a multiple x of some divisor d is also a multiple of all elements in s[d]
nums.sort()
dp = [1] * len(nums)
prev_index = [-1] * len(nums)
max_len = 0
max_index = -1
for i in range(len(nums)):
for j in range(i-1, -1, -1):
if nums[i]%nums[j] == 0 and dp[j]+1 > dp[i]:
dp[i] = dp[j] + 1
prev_index[i] = j
if dp[i] > max_len:
max_len = dp[i]
max_index = i
res = []
while max_index != -1:
res.append(nums[max_index])
max_index = prev_index[max_index]
return res
```