Zaffer Hussain of Bridgefield Drive, Bury was sentenced at Manchester Crown Square to eight months in prison and disqualified from working as a company director for 10 years.
Akbar Hussain also of Bridgefield Drive, Bury was given a suspended sentence of four months in prison and ordered to carry out 200 hours of unpaid community work. He was also given a £3,000 fine.
Both men were found guilty of failure of a director or senior supervisor in their duty to provide appropriate health and safety measures which resulted in the death of Cameron Minshull at Huntley Mount Engineering Ltd in Bury on 8 January 2013.
Huntley Mount Engineering was found guilty of corporate manslaughter and failing to ensure the health, safety and welfare of employees and was fined £150,000.
Lime People Training Solutions, the recruitment firm who placed Cameron at Huntley Mount Engineering, was found guilty of failing to ensure the health and safety of a person other than an employee and was fined £75,000.
Greater Manchester Police (GMP) said: "Cameron began working at Huntley Mount Engineering on 3 December 2012 after being placed there on an apprenticeship scheme by Lime People Solutions.
"On 8 January 2013, Cameron was operating a Computerised Numeric Lathe, unsupervised, and having been given no meaningful training. He was instructed to perform a task which involved him putting his arm inside the machine whilst it was running, which was made possible due to the safety lock on the machine door being disabled.
"This resulted in Cameron getting pulled into the machine and sustaining severe injuries to his head and face. Cameron was taken to Wythenshawe Hospital where he was sadly pronounced dead a short time later."
Inspector Ben Cottam from GMP's Bury Division said: "The sentencing today marks the completion of a joint investigation between GMP and Health & Safety Executive spanning almost two and a half years.
"It has been a sad and difficult investigation for all involved but I'm pleased that the result has been that those responsible for Cameron's death have been held to account.
"I hope that Cameron's family can take some solace in the sentencing, although of course nothing could ever make up for losing him."
He added: "From my point of view this case serves as a chilling reminder of the dangers of placing apprentices in potentially dangerous work environments, and I hope that it can prompt companies and recruitment agencies operating in this field to review their practices to ensure nothing like this can happen again."
