local mce, mfl, msq, mmi, mma, mab = math.ceil, math.floor, math.sqrt, math.min, math.max, math.abs

local function getprimes(x)
  local primes = {}
  local allnums = {}
  for i = 1, x do allnums[i] = true end
  for i = 2, x do
    if allnums[i] then
      table.insert(primes, i)
      local lim = mfl(x / i)
      for j = 2, lim do
        allnums[j * i] = false
      end
    end
  end
  return primes
end

local function getdivisorparts(x, primes)
  local prime_num = #primes
  local tmp = {}
  local lim = mce(msq(x))
  local primepos = 1
  local dv = primes[primepos]
  while primepos <= prime_num and dv <= lim do
    if x % dv == 0 then
      x = mfl(x / dv)
      local cnt = 1
      while x % dv == 0 do
        x = mfl(x / dv)
        cnt = cnt + 1
      end
      table.insert(tmp, {dv, cnt})
      lim = mce(msq(x))
    end
    if primepos == prime_num then break end
    primepos = primepos + 1
    dv = primes[primepos]
  end
  if x ~= 1 then
    table.insert(tmp, {x, 1})
  end
  return tmp
end

local primes = getprimes(400000)
local q = io.read("*n")
for iq = 1, q do
  local x = io.read("*n")
  local v = false
  for i = 1, #primes do
    local p = primes[i]
    if x % p ~= 0 then
      v = p
      break
    end
  end
  local ans = 1 * v
  ans = ans * x
  local dvp = getdivisorparts(x, primes)
  local tot = 1
  for i = 1, #dvp do
    tot = tot * (1 + dvp[i][2])
  end
  local function DIG(i, rem, v)
    local p = dvp[i][1]
    local z = dvp[i][2]
    if i == #dvp then
      if z + 1 <= rem then
        for j = 1, rem - 1 do
          v = v * p
        end
        if v < ans then ans = v end
      end
    else
      -- (z + 1) * 2 - 1
      for j = 1, z - 1 do
        v = v * p
      end
      for j = z, 2 * z + 1 do
        v = v * p
        if rem % (j + 1) == 0 then
          DIG(i + 1, mfl(rem / (j + 1)), v)
        end
      end
    end
  end
  if 1 < x then
    DIG(1, tot * 2, 1)
  end
  print(ans)
end