Google Inc. is making it tougher for computer hackers and other imposters to break into e-mail accounts and other password-protected services.An additional security measure introduced Monday will require typing a six-digit code after an accountholder’s Google password is entered. The codes will be sent to people’s mobile phones.The two-step process means it will take more than a password to get into an account, at least the first time that an attempted login is made from a particular computer. After logging in, users can ask Google to remember that their identity has been verified on that device and security codes won’t be required to get into the account again.The system is similar to that employed by some banks for online account access. The extra protection initially will be offered to companies and government agencies subscribing to a Google service that provides e-mail and other office applications. Google also is offering the added security to schools that rely on Google to run their e-mail systems.People using Google’s free Gmail service will have the option of making the security codes a part of their login process within the next few months. That could turn the security codes into a mainstream staple, given that Gmail had more than 185 million active accountholders worldwide in July, according to the most recent data from the research firm comScore Inc.To make it easier to get the codes, Google has created a free security application for Apple’s Inc.’s iPhone, Research In Motion Ltd.’s BlackBerry and phones running Google’s own Android software.Google wants more companies, government agencies and consumers to feel comfortable about “cloud computing,” — which involves storing vital information on remote servers reached through the Internet.Many people pick simple passwords, which makes it easier for hackers to break into an account. Requiring a security code that’s only sent to the accountholder’s mobile phone erects a new roadblock.Not even the security codes will be enough to protect people’s personal information from some trespassers. For instance, Google has acknowledged it fired an engineer in its Kirkland, Wash., office after he abused his privileges to peer into the accounts of four minors.