Yes that operation was changed in 8.25 to ensure atomic output,
thus allowing one to run multiple factor processes in parallel
and collate the output.

I'll look at disabling this internal buffering if the output is line buffered
(which it will be if outputting to a terminal, or if stdbuf -oL is used)

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https://bugs.launchpad.net/bugs/1620139

Title:
  factor buffers output when run interactively

Status in coreutils package in Ubuntu:
  New

Bug description:
  When the "factor" utility is run without any arguments, it reads
  numbers from stdin and writes the factors to stdout.  One use case for
  this mode is to run factor in a terminal window and enter numbers
  manually.  This worked well in coreutils 8.23 and earlier.  However,
  in coreutils 8.25, the output of factor is buffered, making this mode
  of operation less useful.

  Notice that in the logs for version 8.25, all of the output occurs
  after end-of-file has been reached on stdin.

  I entered the following input:
    factor --version
    factor
    5
    7
    9
    ^D

  bash$ factor --version
  factor (GNU coreutils) 8.23
  Copyright (C) 2014 Free Software Foundation, Inc.
  License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.
  This is free software: you are free to change and redistribute it.
  There is NO WARRANTY, to the extent permitted by law.

  Written by Paul Rubin, Torbjörn Granlund, and Niels Möller.
  bash$ factor
  5
  5: 5
  7
  7: 7
  9
  9: 3 3
  bash$ 

  bash$ factor --version
  factor (GNU coreutils) 8.25
  Copyright (C) 2016 Free Software Foundation, Inc.
  License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.
  This is free software: you are free to change and redistribute it.
  There is NO WARRANTY, to the extent permitted by law.

  Written by Paul Rubin, Torbjörn Granlund and Niels Möller.
  bash$ factor
  5
  7
  9
  5: 5
  7: 7
  9: 3 3
  bash$

  ProblemType: Bug
  DistroRelease: Ubuntu 16.04
  Package: coreutils 8.25-2ubuntu2
  ProcVersionSignature: Ubuntu 4.4.0-36.55-generic 4.4.16
  Uname: Linux 4.4.0-36-generic x86_64
  ApportVersion: 2.20.1-0ubuntu2.1
  Architecture: amd64
  CurrentDesktop: KDE
  Date: Sun Sep  4 23:32:33 2016
  EcryptfsInUse: Yes
  InstallationDate: Installed on 2013-08-13 (1118 days ago)
  InstallationMedia: Ubuntu 12.04.2 LTS "Precise Pangolin" - Release amd64 
(20130213)
  SourcePackage: coreutils
  UpgradeStatus: No upgrade log present (probably fresh install)

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