Add more recipe tests. Make the factor() recipe a bit faster and clea…

…rer.

Doc/library/itertools.rst

@@ -1049,11 +1049,10 @@ The following recipes have a more mathematical flavor:
  # factor(1_000_000_000_000_403) --> 1000000000000403
  for prime in sieve(math.isqrt(n) + 1):
  while True:
- quotient, remainder = divmod(n, prime)
- if remainder:
+ if n % prime:
  break
  yield prime
- n = quotient
+ n //= prime
  if n == 1:
  return
  if n > 1:
@@ -1354,6 +1353,12 @@ The following recipes have a more mathematical flavor:
  >>> set(sieve(10_000)).isdisjoint(carmichael)
  True
 
+ >>> list(factor(99)) # Code example 1
+ [3, 3, 11]
+ >>> list(factor(1_000_000_000_000_007)) # Code example 2
+ [47, 59, 360620266859]
+ >>> list(factor(1_000_000_000_000_403)) # Code example 3
+ [1000000000000403]
  >>> list(factor(0))
  []
  >>> list(factor(1))