Another extremely popular option for both Android and iOS is Dashlane. Mostly because along with being an excellent password manager, it's also an excellent mobile wallet. Plus, they have what they call an unparalleled 256-bit AES encryption.
They consider their app the #1 password manager for Android, and it certainly comes close. You get the usual cloud sync to other devices you own, backups so if you lose your device all the passwords and logins are saved, cross-device compatibility, and other things.
Perhaps the best part here is the built-in browser so you'll never have to worry about whether or not a website or app will be compatible with your apps auto-fill feature. It will always be able to fill in forms for logins and passwords.
In closing, Dashlane is possibly the best Password Manager for someone wanting to use almost all of the features, on a single device. Like their smartphone. It'll store 50 passwords for free.
However, if you want to have full access and use multiple devices or family sharing there's a subscription, as expected, and it's between $5-10 a month depending on your needs.
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